Realist, not conformist analysis of the latest financial, business and political news

Resolved, The Laffer Curve Exists

Credit – public domain

The Laffer Curve is the contention that there is a tax rate which maximises revenue collection. That’s all it is too. It does not claim – although Art Laffer often does – that this rate is lower than the current one. It just claims that there is a revenue maximising rate.

Underneath the hood there is the joint influence of two processes. Some folks live and work on the basis that there’s a certain income they must have and so they’ll work long enough to get it. Raise their tax rate and they might well work longer. This is the income effect and it’s known that taxi drivers – and thus we assume many other pieceworkers – often do work to this stricture.

There are also people who look at the marginal income from the extra piece of effort and think, well, if I’m only going to get that tiddler portion then I’m off fishing instead. This is the substitution effect.

We’re all subject to both effects. What happens to tax revenues overall depends upon how many of us, how much, react according to either idea when taxes change.

A useful guide is that the lower paid are more driven by the income effect, the higher by the substitution. This isn’t absolutely true but it’s a useful guide.

There are those who absolutely deny that this happens at all. They are wrong:

Official NHS data show that 1,358 GPs and hospital doctors retired early in 2020-21 – up from 401 in 2007-8.

The British Medical Association (BMA) said changes in tax regulation were one of the main reasons doctors were choosing to retire early.

The data show the average age of retirement fell during this period, from 61 to 59. And the number retiring because they had reached retirement age fell from 2,030 in 2007-08 to 1,594 in 2020-21.

Even The Guardian is nothing it:

The number of doctors retiring early has more than trebled since 2008, prompting fears that burnout and high pension tax bills are prompting medics to leave the NHS.

Doctors gain both good salaries and also very decent indeed pensions. Combine this with a limit on lifetime pension pots and we get, in those final years of a doctoral career, bowelquakingly high marginal tax rates. So, doctors withdraw their labour – the substitution effect.

The Laffer Curve is true. That a tax rate can be too low to maximise revenue is obvious and trivial. But we now have proof that it can also be too high. Therefore there must be that peak.

What the peak is is still up for grabs of course. But the existence is proven.

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Esteban
Esteban
4 months ago

I did notice that they cite “burnout and high pension tax bills” for the sudden rise. They don’t explain why the impact of burnout would have changed, though. Seems that they had to have something else to lump in there, couldn’t leave the impression that a tax increase was a bad thing without some hope to explain it away.

A bit like the mayor of Chicago blaming their increased murder rate on Indiana. Of course, Indiana hasn’t moved and there’s been no change there that would explain Chicago’s murder rate, but hey, can’t be her fault.

Spike
Spike
4 months ago
Reply to  Esteban

Why, yes there is: A sudden inflow of productive and high-earning people from Chicago (and elsewhere in Illinois).

jgh
jgh
4 months ago

If they won’t choose to work, we’ll just force them to work, dammit. The NHS is the national religion, working for it should be a sacred duty regardless of the financial consequences.

dodgy geezer
dodgy geezer
4 months ago
Reply to  jgh

Addressing the issue by considering tax, we broadly have two approaches.

1 – lower the final rate of tax
2 – up the earlier rate of tax.

Which one do you think they’ll choose?

John B
John B
4 months ago

Doesn’t the fact that there are more women doctors have a significant effect? Women doctors are usually married to high status/income husbands usually up to ten years older and who will retire on a good pension before them.

Women doctors may be inclined to retire when their husbands do also on a decent pension, to spend time together enjoying their money.

if so it’s a triumph for getting that gender balance right in the workplace. Please, no: not unintended consequences!

john77
john77
3 months ago

If you accept that people will starve to death if they have no money to buy food when the tax rate is 100%, then it is indisputable that there is some rate between 0% and 100% that maximises tax revenue. That is elementary logic. Whether the so-called “Laffer curve” is actually a curve or a disjointed series of lines and points is not something that needs to be known – although determining the optimal tax rate would be easier if it turns out to resemble a dromedary’s back.

Spike
Spike
3 months ago

Taxes went up (even when styles as a cap on income) and the number of practicing doctors went down. Respectfully, the two facts are not “proof” of anything, because there may be other factors. Previous replies list a few. Two others happening in the US since ObamaCare are: docs forced out of private practice and into the shelter of a corporation by inscrutable new rules; and docs forced to divert time from patient care to data entry meeting gov’t’s (shifting) rules.

Charles
Charles
3 months ago

The Laffer Curve is a mountain of error from top to bottom. Firstly, the Laffer Curve is not the contention that there is a tax rate which maximises revenue collection. That is saying that a curve is a point, which is clearly wrong. But even so, this is such a small error on top of the mountain that it is like adding the height of a mountaineer standing on the summit to the height of the mountain itself. The Laffer curve depends on various assumptions, some of which are rather dubious and some of which are clearly false. Suppose a… Read more »

Spike
Spike
3 months ago
Reply to  Charles

No, the Curve is not a point. But a curve has a maximum and that is a point.

No, tax policy isn’t the only factor and the curve doesn’t guarantee that tax increases will be counterproductive. But it’s a useful point given that all you people, even “centrist” Manchin, tout a repeal of the Trump tax cut to “raise money” to “pay for” things.

No, we shouldn’t be targeting the Laffer maximum, but a lower tax rate below that at which taxes start wrecking productivity beyond the benefits of a larger Parasite Sector.

Charles
Charles
3 months ago
Reply to  Spike

A curve does not necessarily have a maximum, and in any case as I pointed out, there is no curve.

john77
john77
3 months ago
Reply to  Charles

Are you just trolling or are you really that ignorant? There are only two possibilities – either all tax rates produce identical tax receipts or there is one tax rate that produces the maximum. You do not know that there is no curve and, as I said earlier, it is not necessary for the function Tax Receipts = f(tax rate) to be a curve in order for it to have a maximum. It is absolutely a fact that every curve has a maximum (which may be infinity) as the only function that does not a have a maximum is y=… Read more »

Charles
Charles
3 months ago
Reply to  john77

I’m not the ignorant one – you’re the person claiming that every curve has a maximum. What’s the maximum in the closed interval 0..1 of f(x) = x if x < 0.5, x/2 if x >= 0.5?

john77
john77
3 months ago
Reply to  Charles

That is extremely simple: there is one maximum of 0.5 when x=1 as f(x) < 0.5 if x<0.5 and f(x) =0.25 if x= 0.5. BUT that is not a curve – it is a discontinous function comprising two straight lines. Not that it matters – if you had been competent enough to phrase the question correctly so that the function had two maxima that would not affect the statement that every curve has a maximum – I did *not* say that it had a unique maximum. You missed out the “=” after the comma I think that you have just… Read more »

Charles
Charles
3 months ago
Reply to  john77

I did make an error, but it was to go back an change “open interval” to “closed interval” as I thought you’d have an objection to that. If I had left it alone, there would have been no maximum. There is no reason to suppose that every curve is continous. Even when dealing with something as mundane as money, there’s a reason why you see lots of prices at $9.99 rather than $10 – phychologically there is a discontinuity there.

john77
john77
3 months ago
Reply to  Charles

Since money amounts are discontinuous there really is, not just psychologically, a discontinuity.

Well, yes, I should have objected if you had described a closed interval as an open interval – that would have been cheating. But there would still have been a maximum, actually two maxima, as the value asymptotically approached 0.5 as x approached 0.5 and 1.

Did you ever study any Euclidean geometry? It would have helped you to think logically.

Charles
Charles
3 months ago
Reply to  john77

It does not have a (local) maximum at 0.5 – the function’s value there is 0.25 – less than f(0.49) = 0.49.

And In have studied plenty geometry – though analysis is more relevant here.

john77
john77
3 months ago
Reply to  Charles

Are you a troll or an idiot? I said “as it asymptotically approached 0.5” not “at 0.5”.

Charles
Charles
3 months ago
Reply to  john77

It never gets to 0.5, so that’s not a maximum.

Feel free to invent a whole new alternative mathematics if you like, but I don’t expect any mathematicians will adopt it.

john77
john77
3 months ago
Reply to  Charles

Can you read? f(x) is 0.49999recurring at x=0.49999recurring and x=0.99999recurring. These are maxima. I haven’t invented anything – aymptotes have been part of mathematics since before I was born. It can be shown by logic that, unless all values of a function are equal than the function has a maximum value (or maxima – it does not need to be unique). Laffer made his name by pointing out this elementary fact could be used to demonstrate that some value of TR maximised the yield from taxation. Anybody who tries to argue against a mathematical theorem is either ignorant, stupid or… Read more »

Charles
Charles
3 months ago
Reply to  john77

0.49 is not a maximum, because 0.499 is bigger. Similarly for any other value which in decimal starts with 0.49 and some number of nines. 0.4999 recurring is equal to 0.5, so the function does not have a maximum there as f(x) = 0.25.

john77
john77
3 months ago
Reply to  Charles

Liar, 0.49 recurring is *not* equal to 0.5, nearly but not quite. I am now going to waste my time by setting out the proof of the utterly obvious fact that the function has maximum. If the function y=f(x) is not a constant themn it has a maximum. Proof: take point x(0) and find another point x(1) for which y(1)= f(x(1)) is not equal to y(0)=f(x(0)). then either y(1)>y(0) or y(1)<y(0). Choose the greater of y(0) and y(1) and seek another point x(2) so that y(2)=f(x(2)) is greater than y(0) and y(1). If there is no such point that the… Read more »

john77
john77
3 months ago
Reply to  Charles

“The Laffer Curve” is shorthand for the claim that there is a maximum value of the tax take which is a mathematical certainty. The tax take at 0% is zero. As I have pointed out above there doesn’t have to be a curve (it just makes estimation easier if there is). It does not claim that the tax rate that generates the maximum is invariable across time, nor across countries. It claims that at any given moment for any given taxation jurisdiction there is a tax rate that maximises the tax received. A marginal tax rate of 100% is not… Read more »

Charles
Charles
3 months ago
Reply to  john77

As I pointed out, it is not a certainty of any kind. Insofar as you handwave to narrow it down enough that there might be a maximum (though you don’t actually get that far) you render it nonsense. If you have to constrain it to the point where you cannot use it to model reality, it is useless I didn’t mention marginal tax rates. I was only referring to a single tax rate. If there is a single tax rate then taxation at 100% means the state takes everything. If you want to complicate things by having different tax rates… Read more »

john77
john77
3 months ago
Reply to  Charles

Firstly, every curve has a maximum. A horizontal straight line is not a curve. If you don’t know enough not to expose your abysmal ignorance, you must expect to be a laughing-stock. Secondly I pointed out that the so-called Laffer curve does not need to be a curve or even continuous to have a maximum – it merely needs a single non-zero value to achieve that condition. Thirdly, I didn’t handwave, so stop slandering me. Fourthly, in order to model reality one has to consider each tax jurisdiction separately because only the would-be world dictators of the “Tax Justice Network”… Read more »

Charles
Charles
3 months ago
Reply to  john77

I’ll skip most of that nonsense as I would just be repeating myself, and go straing for point six. Just because some tax avoidance schemes were shut down does not mean that every such scheme was. And for some types of tax avoidance there is a setup cost and minimal running costs, so once the scheme is set up there is no reason to stop it if taxes fall. You’re also failing to consider one of the major ways of avoiding tax – emigration. If you emigrate due to what you feel is excessive taxation, having incurred the expense of… Read more »

john77
john77
3 months ago
Reply to  Charles

It isn’t nonsense – as you presumably know or you would be crowing about every single error that you could find. So it is obvious that you are just being insolent because you haven’t got anything that even looks like a good answer. Emigration? The situation in Ireland in 1850 was different from that in 1840 – who is surprised by that? Are you trying to say that the “Laffer Curve” is invariant over time? Nobody who knows what they are talking suggests that. I have never done so and I don’t know anyone who has. In the 1970s, the… Read more »

Charles
Charles
3 months ago
Reply to  john77

“Are you trying to say that the “Laffer Curve” is invariant over time? Nobody who knows what they are talking suggests that. I have never done so and I don’t know anyone who has.” Well pop over to Expunct and see Tim basing an argument on exactly that: “The insistence in 2010 was that 45% at £150k was the peak of the Laffer Curve. Given inflation and general wage increases since then this must mean that it’s above that peak.”. So no allowance for any possibility that the curve might have changed. I’m not arguing against the existence of a… Read more »

john77
john77
3 months ago
Reply to  Charles

What?!? You are quoting Tim as saying that the peak has moved to justify a claim that he says that the rate setting the peak is invariant! YMBJ Of course tax receipts are determined by a multiplicity of factors BUT, given a set of factors then there is a peak value of tax receipts as a function of marginal tax rates. THAT IS A FACT. National Insurance is a tax on workers below state pension age and Gordon Brown’s pretending that the 2% addition to “National Insurance” was not an income tax was not simply dishonest but also unfair as… Read more »

Charles
Charles
3 months ago
Reply to  john77

“The concept of the Laffer Curve is that there is a maximum level of tax receipts”. Maybe it is. But in that case it’s an assertion dressed up in bogus mathematics.

Charles
Charles
3 months ago
Reply to  Tim Worstall

No one cares because it’s just a rhetorical trick. And a bad one, since someone taken in by it may later realise it’s bogus. It’s fundamentally a mistake – like arguing with a burglar over what he should steal instead of coming straight out and saying stealing is wrong. Just say that taxation can be excessive. And even if there was a maximum, you might have a situation where under one scenario an economy produces $1 trillion of value, with $0.3 trillion taken in tax (30%), which could be switched to anoth where $0.8 trillion of value is produced and… Read more »

john77
john77
3 months ago
Reply to  Charles

Rubbish!

It is an observed fact with the supporters driven to use a mathematical identity to demonstrate that it is a fact in the face of ideological advocates of the demonstrated fallacy that a rise in %age tax rates always leads to a higher amount of tax receipts.

I have reason to doubt whether you know the difference between mathematics and bogus mathematics

Perry de Havilland
3 months ago
Reply to  Charles

That is not just a daft analysis of the Laffer Curve, it is daft at great length.

Spike
Spike
3 months ago

It is a strident attempt to ridicule the notion that there is a principle under which raising tax rates might not always be a good idea.

Charles
Charles
3 months ago
Reply to  Spike

Not at all. It is merely ridiculing the idea that a bogus argument against high taxes should be used instead of a valid one.

MrVeryAngry
MrVeryAngry
3 months ago

My GP did exactly this. We’d chatted about his ludicrous Lifetime Allowance tax charges and he jacked it in in mid 2020. He was young enough to keep going for quite a few years. I should also say that he was thoroughly fed up with the NHS bureaucracy and bullying and the discourtesy of some of his patients.

Quentin Vole
Quentin Vole
3 months ago
Reply to  MrVeryAngry

Most GPs would find their work highly congenial, were it not for those pesky patients. Luckily, Covid means they no longer have to deal with the public.

MrVeryAngry
MrVeryAngry
3 months ago
Reply to  Quentin Vole

Ho ho. True. true. In the same that business would be great if it were not for people, paperwork and customers.

To be fair my bloke was not like that at all. He saw me through a very nasty health scare with great concern, professionalism and care.

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