A point for discussion

As Mr. Redwood points out: the higher, 28%, CGT rate is associated with a fall in CGT revenue of £500 million.

28% CGT is thus over the peak of the Laffer Curve.


64 thoughts on “A point for discussion”

  1. Is there really a Laffer Curve? The economy is a dynamical system; it is non-linear. Is it thus reasonable to draw any kind of curve which implies linearity?

    Take the example of supply and demand curves. Decades ago, Henry Hazlitt cautioned us not to believe that these curves really exist; if one could see the “curve” it would be constantly snaking and snapping about, not some nice tidy relation. They are simply an aid to visualising economics, and it is a fundamental error to believe that one can actually calculate the shape of such a curve.

    Is it thus appropriate to think that one can declare where upon such a non-existent curve one currently is?

  2. Far be it for me to decry the Laffer curve, but isn’t it a bit soon to pronounce on this CGT rate? Firstly its only projections of revenue for one year vs actual revenue for one year. Then you’ve got the fact that the economy is on its knees – there are hardly going to be oodles of profitable investments being liquidated that would have to pay any CGT, whatever the rate.

    I am sure that you are right – that over the cycle, a higher rate of CGT would depress revenue over a lower one. But this is no proof one way or the other.

  3. Ian, how would the curve imply linearity in any way?

    Simplified representations of the Laffer curve are often displayed with the peak at 50 % and the curve is presented with a symmetric parabolic shape, but this is of course just a simplification. Depending on the curcumstances and on the kind of tax being discussed, the peak can be practically anywhere between 0 and 100 %, and in real life it wouldn’t be symmetric, of course. Absolutely no one is suggesting that, so you and Hazlitt are beating a straw man.

  4. Pjt, a curve is inherently linear. A linear equation is one in which you have some relation y=function of x, so you can plug in an x and get a y. A non-linear system is one which is not described by such equations.

    I’m not sure what you think the word “linear” means in this context, but I mean it in the mathematical sense, and from your response you seem to think I meant something different.

  5. JustAnotherTaxpayer

    This one is silly, Redwood should know better.

    2011-12 receipts are strong because of strong equity price rises in 2010. Expected CGT returns are predicated on future equity price changes, and those are expected to be grow in line with NGDP.

    Therefore, future returns will be lower than current returns if recent equity prices have grown stronger than expected future equity price changes.

  6. JustAnotherTaxpayer

    Here are the CGT numbers from the OBR forecast, £bn

    2009-10 2.5 (outturn)
    2010-11 3.2
    2011-12 3.4
    2012-13 2.9
    2013-14 3.7
    2014-15 4.6
    2015-16 5.1

    I see a blip in 2012-13, and no obvious laffer curve positioning issue.

  7. IanB: I don’t think you’re expressing the mathematical concept of linearity very well at all there. Better to stick to the idea that the economy is dynamic, quite possibly chaotic, and therefore things like the optimum taxation point will shift around quite a bit.

  8. Well, I’m a nutter who hangs around blog comment sections, not a math teacher.

    The general point is that there isn’t an “optimum taxation point”. Trying to do arithmetic with a non-linear system that can’t be described by arithmetic leads to the creation of such mirages. You can describe the underlying principles of operation of the system, but that is all. It is as inherently hopeless a task as trying to predict the temperature in Northampton at 12pm on this date next year. Or even, one week from today.

    Tim adds: Ian, you’re not quite getting the point of this Laffer Curve thing. We’re not trying to say that the tax rate should be 18%, or 18.25%, or 17.5%. We’re trying to rule out insanities like 70%.

    At which point let’s try estimating the temperature at noon in Northampton in a week. It’s not going to be -50 o C. Not going to be 50 oC either. In fact, we’d all place a reasonably good bet on it being between 10 and 30 oC. That’s without even looking at historical records for the temp in Nothampton in August at noon. We might refine it a bit more if we did.

  9. Counterpoint: the stated objective in raising the higher CGT rate was not to increase revenune from CGT. It was to stop people avoding income tax by declaring lower taxed capital gains, of which there was much evidence of.

    A decrease in CGT receipts could easily be evidence that this stated policy is working well. We would need to see the income tax vs CGT comparison.

    Redwood is being very disingenuous when saying the revenue level has fallen when he knows full well that that was the stated objective of the policy (I watched the debate on t’telly, he was in it and spoke at length on the subject).

  10. IanB: Yes, I think we’re probably all on board with the idea that the economy moves and changes rapidly, and that therefore making predictions about it is not easy.

    But I would suggest that if you want to be taken seriously, it is best not to claim to use technical vocabulary in its technical sense when you plainly haven’t the first clue what that is. (Just drop the phrase ‘non-linear’, seriously. Such systems can often be described ‘arithmetically’, as you put it; it is their solutions with which we struggle.)

  11. Philip, any time you get around to making some sort of substantive point, I’ll be eager to answer it. Until then, please understand that your ignorant pompous prig approach doesn’t really come across very well on the internet, you know.

    Learning the difference between arithmetic and mathematics would probably help too.

  12. Tim:

    A theory that only rejects the absurd is not much use. With the Northampton example, we already know from historical precedent that sub-Siberian temperatures never happen, so a theory that excludes -50C hasn’t told us anything new. It hasn’t improved our predictive power at all.

    And if the warmists are right and the Gulf Stream suddenly shuts down due to Artic runoff, then -50C might enter into our plausible range anyway. Which sort of strongly demonstrates the whole point about the climate being a non-linear system.

    To go further on the point my poor prose has apparently failed to make, and regarding Philip’s polite criticism, I’ll put it another way-

    Post-classical economics is based on two assumptions, to whit that

    (a) aggregate statistics can be objectively defined and accurately measured

    (b) simple arithmetical (linear) relationships can be discerned between these aggregate statistics.

    Neither of these things is actually true. It is possible to make statements like, “if you increase the money supply you will probably get inflation”. But it is intrinsically impossible, however much data you have, to predict what quantity of inflation, or where it will strike in the economy, or how fast, or the shape of the future price curve. These things are intrinsically unknowable, no matter how much data you have.

  13. So Much For Subtlety

    Ian B – “a curve is inherently linear. A linear equation is one in which you have some relation y=function of x, so you can plug in an x and get a y. A non-linear system is one which is not described by such equations.”

    Sorry but I am not sure that is quite true. A linear relationship is some where you have some function y which is *proportional* to some other function x. That is y(t) = a*x(t) where a is some constant.

    Not one where the equation is solvable.

    A circle is non-linear and yet you can describe that with such an equation. As are parabola.

    Linear equations do tend to be solved easily. But it is not a condition. These are two very different things. Non-linear equations are often solved in the sense you mean. They would not be much use if they didn’t.

  14. SMFS

    I am clearly paying a heavy debating price for trying to oversimplify to get a point across. My bad.

    linear relationship is some where you have some function y which is *proportional* to some other function x.

    That is what I said. y=f(x) where f is some mathemetical function. For a circle,




    y and x have a linear relationship. This is not true where y and x are two economic variables.

  15. “A linear equation is one in which you have some relation y=function of x, so you can plug in an x and get a y. A non-linear system is one which is not described by such equations”: oh dear, oh dear.

    Anyway, in the context of dynamical systems, the focus is usually on linear and, especially, nonlinear differential equations, not algebraic equations. However, you can learn heaps by playing with simple nonlinear difference equations, particularly the one most usefully written as

    x(n+1) = Ax(n) [1-x(n)]

    where you should calculate the sequence that arises for different values of A and for different values of x(1), and contemplate the results.

    Alternatively, hue to Dearieme’s Second Law: “When (almost) anyone talks about “nonlinearity”, it’s as if he’s talking about “quantum theory” or “relativity”: to wit, he’s talking shite.

  16. I fear I am among a gaggle of aggregate stat fans, fearful that if the truth gets out about the economy, they’ll lose out on the excitement of pronouncing that if you do this, you’ll get that.

    It’s striking to note how discussions like this rapidly devolve into insults of the “U is ignerant” kind. Always a good sign of insecurity. Hey ho.

  17. Arnald, people believe in whatever theory apparently gives them the answers they want. For instance, people who want high government borrowing and spending believe in “stimulus” even though that is demonstrably bunkum.

    For much the same reason in fact; the belief that there are arithmetical relationships between aggregate statistics, and thus the belief that modifying one such statistic will produce a predictable change in value of another one.

  18. But Arnald, my point wasn’t about whether the Laffer curve was bunkum or not, it was about the fact that this blog’s stupidest commenter by far thinks simply declaring it is rubbish is going to convince anyone of anything.

    Do you see what Ian B has been doing above? Its called “an argument”.

  19. “Stupidest commenter”.

    Oh my. Worldview feeling a trifle threatened there is it Chris?

    Look, there are lots of good arguments for free markets, but clinging to imaginary graphs just doesn’t get us anywhere. There isn’t a Laffer Curve. Just get over it.

  20. Oh wait a minute, you weren’t having a go at me and…

    Sorry, I need to climb out of this bunker. I really am this blog’s stupidest commenter.

    I apologise Chris, and will now slink away glowing red with embarrassment.

  21. @IanB for the avoidance of doubt, I was not referring to you.
    I must admit I thought that was obvious by virtue of the fact I contrasted his method of “debate” with your own – which is a proper argument.

    I am not calling Arnald stupid because of threats to my world view, I am calling him stupid because he continually makes stupid comments.

    You and he are clearly in agreement on the Laffer curve, but whereas your comments are worth reading (the old argument thing), his are – as ever – pointless.

    To call a belief in the laffer curve – or otherwise – a “world view” is a little bit strange. Its hardly a “world view”.

    “Just get over it” is a really juvenile turn of phrase by the way, and not worthy of you.

  22. No apology needed Ian, but I’ll accept it so as not to be churlish. (Big fan of Counting Cats by the way).

  23. In the interests of peace and harmony I’d just like to point out that actually I’m the stupidest commentator here, I’ve worked hard for that position by commenting on things I know little or nothing about, I’m not giving it up for amateurs like Arnald.
    Just a query Ian B, if as you say people believe in the theory that gives them the answer they want and I’m inclined to agree, how can you say so definitely that the idea of stimulus is bunkum ? Doesn’t that view arise from adherence to a counter theory and if it doesn’t then presumably we’re back in the world of relativity where nothing has any objective reality.

  24. IanB, I assure you that your definition of ‘linear’ is not one that any mathematician would recognise. SMFS is correct, and the key in their definition is that ‘a’ is a constant for each relationship. y = 5x is an equation where x and y have a linear relationship (a=5): y = x^2 is not because you cannot pick any constant a to make both 4 = 2a and 1 = 1a true (picking the points x=1, x=2 on the curve).

  25. Yup Arnald is a dumb schmuck.

    But to dismiss the concepty that there’s an optimum level of taxation – and it’s obviously not 100% is ignorant.

    Mrs T proved this when she abolished the 70’s Labour rates and revenues rocketed…

  26. Actually there is an optimum level of capital gains taxation – the same rate as income taxation. Otherwise, as MatGB points out, you are creating a distortive incentive capital gains – to which people will react either by changing the nature of their activity, or changing its legal form. Neither is a good idea.

  27. No, it takes brains to convince someone who initially disagrees with you that they are in fact wrong, and you are correct. Being an annoying twat doesn’t require brains at all.

  28. If you find what I write annoying, chrissums, then that’s your problem, not mine.

    You’ve been annoyed from the word go, showing that anyone that voices a contrary opinion (based on real life and not smug self-interest) gets on your goat in a manner that cannot be healthy.

    The Laffer curve is twaddle, why should I have to do your research for you, when the argument is a click away.

    Bring back the birch, crosspatch.

  29. Well actually you are the one with the problem because you annoy everyone here, including those who agree with you on individual points. I have never seen anyone here side with you even when they are agreeing with you. There are quite a few lefties on here, and none of them ever see fit to defend you. If you and I agreed on everything you would still be an annoying prick.

  30. As for self interest, you are a tax consumer who argues for higher taxes. Its quite clear – thick though you are – you know what serves your self interest.

  31. When have I argued for higher taxes!!!!?

    Advocating using taxation to improve the social infrastructure of a nation is not the same as advocating higher taxes. Understanding that taxation is not theft or a voluntary payment to a perceived dictatorship/clown-depot is different to wanting to nobble markets and entrepreneurialism.

    So my point remains, you are annoyed by a false stereotype. That’s you’re problem.

    And you’re wrong.

  32. So you are now saying that you do not believe taxes should be higher than they are now? If this is the case, excellent.

    Anyone who claims to not want to increase taxes, but also wants to see improvements in social infra structure can only be arguing for more efficient spending of existing tax. Again excellent.

    So you want to see no increase in tax, and more efficient spending of existing tax revenue. Hallelujah! I must admit, you have been less than clear in the past that this is what you are advocating. Still there is more rejoicing in heaven over one sinner that repenteth etc.

  33. No chrissums, I just stated you were putting words in my Arnald-worstallblog interface.

    The precise rate of tax depends on what the electorate want it to be, by and large. They can vote for a system that rots the soul, like the current debacle, or for one that does some work and fixes stuff that most of us want.

    It is only from a position of wealth and/or privilege that one can demand slashing taxes and letting stuff decay.

    And that’s what it comes down to. Libertarianism is a stain on humanity. There cannot exist this wonderland where all are free, because libertarianism demands that others carry the can through exerting influence through wealth and privilege.

    To talk about the mythology of economics in its mathematical form and apply it to the deeply divided global population is simply bollocks. That’s why Hayek and all you twats that believe in Chicago school and Austrian stuff are just egoistic sociopaths.

    Society is more complex than consuming and trading. Government is more complex than taxing and law-passing.

    The rot in the west has been caused by sociopaths buying political influence. It’s time for them to shut right up, and that includes twats like Worstall that think life for other people is a joke for him to snide about – likewise the commentators on here that can only slag off ideas and parrot failed theory rather than understanding anything further away than their wallets/cock/hatred. It’s bullshit you repeat over and over again.

    Chrissums, when was the last time you actually posted anything resembling an opinion?

    Bitter, bitter fools.

  34. Hi Arnald, smug ugly faced twat here*. As someone who would broadly describe themselves as libertarian may I be permitted to cross into your looking glass world and enter a plea of not guilty to all those horrible things you’ve accused me of ? I suppose you’d describe yourself as left wing so can you tell me why so many leftists decry stereotyping of others and yet revel in it when confronted with political or economic views that differ from their own ? I don’t recognise myself in any of your descriptions, I support lower taxation and I have worked in manual and semi-manual jobs since leaving education over forty years ago and I’m very far from wealthy, so I should be the sort of person who’s more likely to support your arguments. If the world’s economy goes tits up or even if the Euro collapses ( I’d broadly welcome that ) I stand to be one of the big losers and yet I have no interest in bringing about the sort of carey sharey world that you seem to hanker after and that doesn’t make me a sociopath, just someone with different opinions and preferences. Another question, if you hate this blog and the people who comment so much why do you come here ? Frankly people like you frighten me, we know what happens when those who think like you gain real power, I have no desire for a walk on part in your theatre of the absurd thanks.

    * I’ll grant you the ugly faced twat bit.

  35. Thornavis
    I can only conclude that you are misguided, blinded by the lies.

    If the economy goes tits-up (again) then it won’t be because of anything remotely ‘carey-sharey’ (is that a gum related STD?), but because of the ideology espoused by the likes Worstall. So your irrational dislike for more social policies leads you to form opinions that are counterintuitive?

    “we know what happens when those who think like you gain real power”

    Do ‘we’? Do ‘we’ really?

    I bet your mates call you Oscar Wilde in admiration!! Suckling teats indeed!

    And taxpayers teats to boot!

    Sigh. Ignorance is piss.

  36. Patronising me now Arnald, you certainly know how to win people over, I suppose there’s no chance that I might have given these matters some thought and reached different conclusions from you ? Yes we do know exactly what happens when people with a high moral purpose and righteous anger gain political power, history is littered with examples to choose from.

  37. A further thought Arnald. I reached my present world view having been previously generally left of centre and socially liberal. Eventually it dawned on me that social liberalism was only possible with economic liberalism too, you can’t divide them.

  38. “Eventually it dawned on me that social liberalism was only possible with economic liberalism too, you can’t divide them.”

    I challenge that, but without knowing the terms of reference, I can’t really get going….

    Sounds more like the rich can do what they like at the expense of everyone else…? That’s what the libertarians crave for….

  39. Libertarians crave no such thing, do you imagine that every liberal/libertarian is wealthy ? Doing what you like at the expense of everyone else has been the norm with the powerful since we started living in settled communities and quite probably before. No elite is immune to it, tacking progressive or democratic to the side of the power wagon protects absolutely no one from this reality. I have no time for either corporate or state power and no wish to prosper at another’s expense. Neither do I wish for myself or anyone to be subject to the will of political elites imposed through state force or by the self appointed guardians of righteousness hiding behind the pretence that taking my money and liberty is being done for my own good.

  40. What terms of reference do you want for the social/economic liberalism question ? It seems very simple to me, freedom of action and conscience requires a liberal polity that does not proscribe any behaviour that cannot be shown to cause harm ( not inconvenience or offence ) to others . Economic freedom ie simply keeping as much of your own money to use as you see fit, is a necessary part of this.

  41. Just to clear up a bit of terminology once and for all: a linear function is, as the name suggests, a straight line. It is a degree 1 polynomial function of one variable of the form f(x) = a x + b where a and b are constants. Something of the form f(x) = a x² + b x + c is not linear. It is in this case a quadratic polynomial.

    Additionally in physics/engineering etc., a linear system is one that satisfies the conditions of superposition and homogeneity, which is to say that f(a + b) = f(a) + f(b) and f(k x) = k f(x). The underlying f(x) does not need to be linear in the first sense. It is instead a linear map between domain x and range y.

    And the Laffer curve is predicated on Rolle’s theorem, which states (in its basic sense) that if a continuous, differentiable real-valued function attains the same value at two different point then there is a point in between the two where its first differential vanishes. Since no tax is collected at the extrema, and at least some is in the middle, then there must be a point where the tax take is maximised, if continuity and differentiability hold (which they might well not.) The theorem doesn’t say where that point exists, simply that it does. It may be an oversimplification, but is simply not the case that reduced taxation inevitably reduces revenue and vice versa. It’s begging the question anyway: why should revenue maximisation be the sole aim of tax policy? It just gives bastards like Murphy more power, apart from anything.

    Hope that helps.

  42. “why should revenue maximisation be the sole aim of tax policy? ”

    Sadly for many revenue, maximisation for the treasury is not the sole aim (bad though this would be), rather it is to take as much as possible from those deemed to be “rich”. You only have to listen to spiteful little shits like Arnald to see what the main purpose of taxation is in their eyes.

  43. Oh dear chrissums
    “…maximisation for the treasury is not the sole aim (bad though this would be), rather it is to take as much as possible from those deemed to be “rich”.”

    No, you haven’t got the hang of this ‘tax’ thing at all.

    Spiteful? me? Just fighting textual fire with textual fire, old bean. I get abused everytime I choose to type anything. I don’t care, as long as I can say exactly the same things but cleverer, like.

    “…that taking my money and liberty…”

    ‘Reds under the bed’ a little bit, wouldn’t you say? This is after more than thirty years of bunkum economics that has led us to the worst set of crises for ages. It beggars belief that there is any other analysis.

    “..freedom of action and conscience requires a liberal polity that does not proscribe any behaviour that cannot be shown to cause harm ..”

    Where can I begin? This is such a vacuous soundbite.

    Who and what is ‘harm’?

    At a fundamental level all libertarians would have to live the whole sackcloth-and-ashes thing. The causality of aspirational consumerism predicates a suppression of ‘liberty’ for those servicing that aspiration.

    What you seem to be asking is that you should be free to consume and express as you wish as long as the causal chain is beyond your senses.

    Far better there should be a balancing social conscience, provided through education and knowledge of how ‘liberty’ is used by the powerful to influence our basic needs, that can only be sourced through taxation.

    Being truly liberal requires a great deal of infrastructure. There is an apparent wish from the global megacorps to restrict information and to get the shit you are saying printed all over the mass media.

    You are being led by the nose by ideological spastics.

  44. Unimportant Quibbler

    David Gillies has given an excellent explanation of the difference between “linear” and “non-linear”, which can be very confusing to those without a mathematical background. Just to muddy the waters further, statisticians performing a regression analysis may well fit a polynomial curve such as y(x) = ax^2 + bx + c as the logical extension to the familiar “line of best fit” y(x) = ax + b, if the data seem to follow a curve (here a parabola) rather than a line. This is still, however, classified as a “linear model”! (Because although y is a non-linear, indeed quadratic, in x, it is linear in the coefficients a, b and c. In contrast the model y(x) = a*b^(x) is non-linear in b… although it may be rendered as a linear model by taking logarithms!)

    David’s statement of Rolle’s Theorem in relation to the Laffer Curve is helpful – the conditions necessary for Rolle’s Theorem to apply, themselves imply the limitations we face if we wish to make the “strong” (TPA etc) version of the Laffer statement i.e. if we were able to construct (counterfactually) the curve, would it be “nicely behaved” enough for Rolle’s Theorem to apply? This seems to be what Ian B was grasping at, but lacked the technical language to pin down. Unfortunately “general appeals to non-linearity” are, like appeals to chaos theory, fractals, quantum mechanics, hidden dimensions, parallel universes, evolutionary psychology and econophysics, all too often the marks of a crank. The more intensely praxeologically-inclined Austrian Schoolers would no doubt add “econometrics” to that list!

  45. Christ it’s a job to know where to start with all that, it’s pretty much boilerplate Guardian speak, attributing a number of things to me based not on anything I’ve actually said but on your statist template to which I must be fitted, to call it a strawman would be to insult cereal based mannikins. I do find it rather amusing though that you accuse me of a reds under the bed approach whilst constantly yelling that the sky is falling in and it’s the wicked hard faced libertarians who have knocked the props away, you seem to have your own witchfinding agenda. Then there’s this classic ” Far better there should be a balancing social conscience, provided through education and knowledge of how ‘liberty’ is used by the powerful to influence our basic needs, that can only be sourced through taxation.” What on earth does that mean ? Vacuous soundbite you called my nutshell description of libertarianism, no sense of irony there then. As for being truly liberal requiring a great deal of infrastucture, no it doesn’t all it needs is a recognition of other people’s autonomy and a refusal to attempt to impose my will on them. I really can’t understand your penultimate sentence at all, I think you should do a quick proof read before you post, it might help to get your thoughts down more clearly.
    Anyway must go now as I’ve been up since five earning a crust and keeping the wheels of industry turning, nasty baby eating capitalist that I am. No doubt we will continue this titanic clash of giant intellects at a future date.

  46. I called you spiteful because of your views on the tax and the rich, not because of your “textual fire”*

    * Ahaha, you stupid pretentious twat. “Textual fire”, what a knob. Textual shit is more like it.

    (Comment also meant for Arnald in case there was an doubt)

  47. chrissums
    Har! Why do you bother? You can’t even read, let alone entertain any idea of being able to interpret simple concepts.

    OK so I’ll fight textual shit with textual shit. It’s all the same to me.

    Were you bullied as a child?

  48. For someone who admitted they tried and failed to get a job at a supermarket, its a bit rich to be casting aspersions about anyone else’s intellect. I guess this could be where you get your enormous chip from against anyone who actually achieves anything.

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