Best Curve-Fitting Ever

By Sean Carroll | July 13, 2007 3:03 pm

From Mark Thoma, via Brad DeLong, comes what will henceforth be my absolutely favorite example of twisting data to fit your theories. Observe the following graph of corporate tax rates vs. revenue in units of GDP:


Pretty straightforward, really. As you raise taxes, the government collects more revenue. Norway seems to collect more than its fair share, which might be interesting to dig into, but the trend seems clear. But there’s something nagging at the back of your mind — aren’t there people out there in the world who believe that raising taxes actually decreases revenue past some certain not-very-high tax rate? “Supply-side economists,” or something like that? People who exert a wildly disproportionate influence on U.S. tax policy? What would they make of such a graph?

Yes, Virginia, there is such a thing as supply-side economics, and you can find its practitioners in such out-of-the way places as the American Enterprise Institute and the editorial pages of the Wall Street Journal. Here is how such people view these data:


No, I am not being unfair. I did not draw the “Laffer Curve” on top of those data in order to embarrass the WSJ or AEI. They did it themselves; the second graph is how the plot was actually published by the Journal, while the first one was Mark Thoma’s subsequent reality-based-community version of the plot. As Kevin Drum says, it’s “like those people who find an outline of the Virgin Mary in a potato chip.”

Among other features, we note with amusement that the plotted curve implies that tax revenues hit zero at a corporate tax rate of about 33%, and become dramatically negative thereafter. As of this writing, it is unclear what advanced statistical software package was used to fit the Laffer Curve to the data; the smart money seems to be on MS Paint.

CATEGORIZED UNDER: Science and Politics
  • Will Diamond

    The best part is that the laffer curve doesn’t even apply to the income as percent of GDP graph. I’d be curious to see the microeconomic reasoning behind such a graph, if there is any. I guess the difference between econ and physics is that this is that this is how econ treats cranks.

  • AgnosticOracle

    Back when I took Economic (circa 1987) my economics 1 professor explained the Laffer Curve like this. Some assistant professor somewhere was having a few martinis for lunch one day. He had this idea that as the tax rate goes up people will more of an incentive to cheat so the effective tax rate (the rate that is actually collected) might climb slower. He then got the idea that perhaps if the tax rate got high enough not only would the effective tax rate decline so would the over all revenue generated. So he drew the curve on his napkin. After a few more martinis and decide that we were on the downward side of the curve.

  • Brad DeLong

    IIRC, Norway’s corporate tax revenues come from excise taxes on the giant pool of North Sea oil. If you take out Norway’s oil boom-related revenues, it comes right down into the middle of the scatter plot.

  • Neil B.

    Ironically, the supposedly optimum value at Norway’s point looks like about 28%, which I think is what Laffer originally thought was optimum. The Laffer curve has to be right ultimately of course, since at very high levels tax rates would have a destructive effect. That of course does not excuse this exercise in deceptive graph manipulation (go to RealClimate to see about similar travesties by global warming skeptics, and of course alternate history creationists do this too.) It is so typical of that right-wing crowd. If you are an honest conservative type, please work for your tradition’s reform or get into a third party, don’t defend hacks like the WSJ propagandists. (Well, what do you expect of people who complain about those who get something for nothing, but whose favorite way of making money is to buy and resell financial instruments – and then they want to pay a lower tax rate on that than those who actually produced new utility value.)

  • mollishka

    That’s fantastic.

  • collin

    I’d love to see the chi^2 on that…

  • Tom

    Pretty straightforward, really. As you raise taxes, the government collects more revenue.

    I have an office building. I raise the rents, I get more revenue. Pretty straightforward, really.

  • Dr.Dichotomous

    Lies, damn lies, and statistics?

  • Gerg

    Ok that’s pretty silly. For that matter picking one particular type of tax and graphing it against all revenue seems whacked. Not the least because those countries have varying amounts of local corporate taxes and other types of taxes such as VAT.

    However AgnosticOracle seems to have taken away precisely the wrong part of his economics lessons. The key observation was that if taxes are 0% then the government gets no revenue, and if taxes are 100% then government gets no revenue (at least barring men with guns coming to force you to go to work). Yet clearly revenue is >0 for tax rates in between 0% and 100%. So there *must* be a maximum somewhere between there.

  • Zeno

    Seldom does one get to enjoy the spectacle of raw data fitted so precisely to theoretical curves. Spooky! And the results explain so much! (They explain that these guys are hilariously blind to the deficiencies of their ideological constructs.)

    Graphs are such useful tools, but you’d think that they would try harder to achieve some level of plausibility. I monkeyed around with deceptive graphing and came up with a graph that plots oscillation as a perfectly straight line. [Link]

  • Jason Dick

    I’d have to second that, collin. But there is no doubt whatsoever that the chi^2 on the second graph is vastly, vastly higher than that in the first. You don’t draw a graph that goes above nearly all of the data points, and vastly below the rest and end up with a decent chi^2.

  • Ian Clarke

    The curve you criticize is a deliberate and cynical manipulation of the data, so you respond with your own deliberate and cynical manipulation of the data.

    Regardless of where the points actually lay, if you insist on drawing a line, and you require that the line goes through 0,0 – then it is inevitable that the line will indicate a positive correlation between corporate tax rate and government revenue.

    The curve fitting you criticize is indeed flawed and manipulative, but so is your line-fitting, because by insisting on a line, you make a positive correlation inevitable regardless of the actual data.

    I think it is pretty obvious that government revenue will decrease above a certain tax rate, because after a point taxation will remove the incentives for doing business, and businesses will therefore move. The interesting question is where this point is, and neither the curve you criticize, nor your own line-fitting, answer this question.

  • Milton F.

    “I think it is pretty obvious that government revenue will decrease above a certain tax rate, because after a point taxation will remove the incentives for doing business, and businesses will therefore move.”

    No, no, you don’t understand where Sean C. is coming from. In the left-wing fantasyland, the purpose of business is not to make money, but to MERCILESSLY EXPLOIT THE DOWNTRODDEN WORKING CLASS, AND ALL MINORITIES. So business will go on, no matter how high taxes are, as long as there is some poor person to be exploited.

    The hilarious thing here, of course, is to object to the WSJ follies on “scientific” grounds, when [for example] welfarism is an experiment that has been tried thousands of times with results varying from pathetic to disastrous. I thought scientific people were supposed to discard theories when they fail experimentally….

  • Sergio Correia

    I agree with Brad. Norway is an outlier so should be taken out. Probably the curve changes a LOT after that country is dropped.

    Also, the regression should include quadratic terms, and as Ian said, should not be restricted to go through the intercept.

  • Joe

    Here’s a different criticism that I think might call the meaning of the graph into greater doubt that we had thought.

    Simplistically speaking, the tax revenue per GDP should equal the corporate profit per GDP times the corporate tax rate. Governments tax corporate profits, not corporate income. The Wall Street Journal article then makes a big deal about interpreting the chart in terms of corporate flight, and a lot of the discussion and comments about it invoke various incentives the tax rate may have to increase or decrease tax revenues.

    The big problem I see is that the interpretation of the curve that we’ve seen so far relies on a hidden assumption: that all of the economies represented by data points on the chart are at the same average level of market development. In the absence of barriers to competition, a young industry with much profit should see that profit decline down to zero as new corporations enter into that industry with time. Or for another example, a nation that just abolished price controls for a consumer good might see a temporary spike in that industry’s profits before new suppliers can begin increasing the supply again.

    So we might want to decide which of these nations are in the throes of a deregulatory binge before we draw any deep conclusions.

  • Sergio Correia

    As a side note:

    We have 7 years of data:

    So including this extra information should give a better approximation.

  • David

    As a physicist I can confidently say the problem with economics is you have plenty of data, you just don’t really have a science that can do anything sensible with it.

  • Joe

    The USA Is Becoming a Police State

  • B

    Hi Sean,

    This is great :-) thanks for once again confirming my prejudices about economists… (sorry! really trying hard to get rid of them, but mostly unsuccessful)

    I just can’t understand complaints about tax rates based on nothing but the percentage, neglecting what one gets for it. The question is not how high the total tax rate is but what the money is used for, and whether this is what the public has democratically decided. If the people in country X want more (public transport? social security? health insurance? unemployment insurance?) to be shared responsibility, the thing to do so is to use taxes. That’s got nothing to do with ‘fairness’ – what the common sensus regards as fair and what not is exactly what the political system should find out, this might very well be different in Norway than in the US.

    The problem with the present tax system is that the actual relation between taxes and what they are used for is too weak. In many cases some taxes are raised to use the money elsewhere. Needless to say, this doesn’t make any sense and results in people not willing to pay taxes because they don’t see what it’s good for. Bottomline is, most people come to the conclusion the lower the tax rate the better. As simple as wrong.



  • Arun

    (sorry! really trying hard to get rid of them, but mostly unsuccessful)

    I will gladly join you in your efforts to get rid of economists! (If there are none, you can’t have prejudices about a non-existent thing, can you?)


  • AJ

    Did anyone bother to look up the fact that this line is not being fit to the data?

    It is merely a curve which indicates ‘good’ ratios are below the curve and ‘bad’ ratios are outiside the curve.

  • Emma

    Richard Feynman said that if had to life live over again, he would have become an Economist. I think perhaps he would reconsider after seeing the way that some physicists treat economics with immature academic snobbery.

    Of course Sean is right and people try and fiddle the data for political reasons, but those of you who just want to piss on economics because it makes you feel better… get a life! Economics is not physical science, people are not atoms, and any modelling that you do in a social science will neccesarily be very approximate because the complexity of real human interactions precludes an exact formal understanding. The question is, have the models of economics helped understand important phenomena, and the answer is undoubtedly yes. You cannot avoid problems just because they are difficult, so give the social scientists a break, they are playing by a different set of rules.

  • Gerard Harbison

    Take out Norway and UAE, both of which are highly anomalous, and the left hand straight line is scarcely more supportable than the idiocy on the right. That in itself is significant; it says corporate taxes appear not to be strongly corrleated with the ability of the government to raise money.

  • Haelfix

    Wow! The premise that raising taxes forever leads to forever increasing federal revenues is ridiculous and absurd. These things have time dependance and are not independant of the state of the economy.

    The Laffer curve is the perfectly obvious (and 100% accepted) observation that zero percent tax has no federal revenue, and 100% taxrate implies zero incentive to work –> another minimum. Therefore in any economy there is at time t, a global maximum.

    Whats not accepted is exactly where that maximum is, and presumably it also could change with time.

    Besides, things are much more complicated than that. During the Reagan administration, taxes were cut and federal revenues hit an all time high. Conversely, Clinton raised taxes, and revenues also hit an all time high.

  • michesmith

    My money is on photoshop. That looks suspiciously like a Bezier curve, which you can’t draw in paint but can draw quite easily with photoshop. Anyway, it seems like he may have assumed a parametrization of the laffer curve based on the mode and then selected the mode using order statistics (ie max). This isn’t completely arbitrary but its still extremely dishonest.

  • Jeff

    AJ points out correctly that the article does not justify the curve as a fit to the data, and only points out whether some countries are on the “right” or “wrong” side of their curves in terms of getting more bang for their tax buck.

    Nonetheless the plot makes it very obvious that this curve has no relationship to these data, and the WSJ should rightly be ridiculed for that. I accept that the Laffer curve must be correct in one form or another, but this data set offers no support to that shape or choice of maximum. Without strong justification of that particular curve from other evidence, the data even argue against that choice of curve.

    It’s apparent that whatever variation there is in this data set has little correlation with that choice of curve, and the use of that plot to justify the articles taxation conclusions is insulting.

  • Steve

    It’s called the abysmal science for a reason. The more one tries to say, “It is so,” the less likely one is to be correct. Sending the tax line through 0,0 isn’t accurate for this reason. The government earns revenues on rents for things such as oil and grazing land leases. Compared to total GDP, they are insignificant I’m certain (I don’t care to look it up) but it proves what some are saying. It seems the only answer to questions like “Which school of thought is correct, the Free-Market economists or Post-Keynesian economists?” (feel free to enter your own school here) is “Yes.”

  • Neil B.

    Aside from what taxation percentages are optimal as such, how about a graduated corporate income tax? I mean, the percent levied on the profit would rise with profit margin (after a deduction, to avoid punishing little companies that have to markup higher to make enough money at all.) Then we reward the industries that serve the public by selling by volume at low profit margin, and penalize the “gougers” without having to directly regulate prices.

  • Chi

    Chi^2 for different types of curves is even more meaningless than the measure itself.

  • aquariid

    Laffer is merely simplistic, i.e. silly. It assumes a mutally exclusive dichotomy between private profit and government revenue. Reality is that gov revenue when appropriately spent increases private profit. Corporations use the “commons” of society as much as (if not more than) individuals.

  • Haelfix

    Yea there are many feedback mechanisms and so forth inherent in the Laffer curve. Which is why it makes talking about where the optimal point is, extremely difficult and academic. Economists talk about being on the left or right of the curve and so forth, but really thats model specific

  • strd

    Soviet Union in the first years of perestroyca and later Russia experimented with summary 70-90% taxes (there were several types of taxes). The result was not only near zero tax revenue, but also complete criminalization of economy – instead of paying taxes enterprises payed protection money to gangs. Eventually about half of Russian economy become property of organized criminals and that become a main obstacle to Russian economic growth.

  • Nathan Parker

    Besides, things are much more complicated than that. During the Reagan administration, taxes were cut and federal revenues hit an all time high. Conversely, Clinton raised taxes, and revenues also hit an all time high.

    My memory from economics is that the Laffer curve is a long-term relationship; whatever short-term results Reagan and Clinton had, the Laffer curve was not involved.

  • Don Cox

    “I have an office building. I raise the rents, I get more revenue.”

    Not if you raise them to four times the going rate in the market. If you do that, all your tenants will move out, and new ones will not move in.

  • Marc S

    In the early 90′s, there was a suggestion that the solar neutrino flux was changing in time, and was anti-correlated with the sunspot cycle (leading to much discussion about neutrino magnetic moments). But it was only based on 15 years of data, and the sunspot cycle, of course, is 11 years. Someone at a conference then showed that the fit was even better if you compared the solar neutrino flux with the number of Republicans in the US Senate….

  • thm

    One thing that can be said about these data is that they lie in a plane.

  • Count Iblis
  • ZBicyclist

    Throw out Norway as an outlier.
    Throw out UAE as an outlier.
    Result: a random cloud of point showing nothing.
    That’s what this really shows, but it’s hard to get a publication out of that.

  • Brian

    The Laffer Curve is a joke. At its most basic, it relies on two assumptions:

    1 — that a tax rate of 0% will bring in $0 revenue

    2 — that a tax rate of 100% will bring in $0 revenue

    Assumption 1 is indisputable. But Assumption 2 is simply false.

    In a society in which all income earned from business is taken by the government in taxes there will still be business activity. The tax revenue is not simply taken by the government and then burned. It is presumably used (at least to some non-trivial extent) for goods or services for the benefit of the country’s people. That benefit is shared at least in very small part by the businesses being taxed (or more specifically the individuals that make up the businesses). That slight benefit is sure to provide enough of an incentive for some business activity.

    I think it is clear that at some point the tax rate reaches a level that is higher than optimal to maximize revenue because of the negative incentives on some businesses. But it is simply not plausible to argue, as the Laffer Curve does, that 100% tax rate will result in $0 revenue.

  • milkshake

    at least all the datapoints are on the same plane… (von Neumann)

  • Habyarimana

    B said: If the people in country X want more (public transport? social security? health insurance? unemployment insurance?) to be shared responsibility, the thing to do so is to use taxes.

    And if the people in country R want to hack a minority group to pieces, the thing to do is to use machetes.

    What you are suggesting is that we ought to rip off the rich in order to buy the votes of the poor. Dear B: you are in the wrong field. You ought to be a politician.

  • B

    Hi Habyarimana,

    No, you are mistaken. Democracy doesn’t mean you ignore minorities to the benefit of the majority, but it gives you a powerful tool to find the best compromise. The notion of ‘ripping someone off’ is very vague, and not worth discussing at all. If you ask me, my personal opinion is that not too much money should be in the hands of too little people since unfortunately we live in a society where money weights influence, and such a distribution of wealth counteracts the very basis of a democratic opinion making process.

    And if the people in country R want to hack a minority group to pieces, the thing to do is to use machetes.

    You should try to find out what a constitution is good for, and why it can’t be changed from one day to the other by a people’s vote. There are places where a direct feedback can be useful, and places where it is completely inappropriate. In economics the feedback given by the customer works very efficiently and very direct, and allows to take this into account in further decisions. This works fairly well to optimize over short time periods, and neglects what might become important only on global distances or long time scales. The political system to outbalance these shortcomings is presently extremely inflexible and unscientific (not to mention not globally functional), it’s a problem that will become more and more serious the more important it will become to correct the outcomes of capitalistic developments. It’s the capitalistic system that, if left unattended, works towards a one-fits-all mediocrity, it optimizes economical growth on the expenses of variables that can’t be easily measured in financial values.

    I choose more than a decade ago not to go into politics but finish my BD in maths, and I have no regrets about where it lead me. As much as I am interested in politics and sociology, it’s an interest that is far too theoretical to be useful for a career in this field, and I not into all these games that are being played there: all the networking, all the decisions that are made behind the scenes, all the senior people that just keep doing things as they have always been done, for no other reason because they have always been done so… wait… does this just remind me of my actual job?



  • B

    Throw out Norway as an outlier.
    Throw out UAE as an outlier.
    Result: a random cloud of point showing nothing.
    That’s what this really shows, but it’s hard to get a publication out of that.

    One could try a random distribution. It seems either the UK or Canada is the most average of all states in this plot, EH? Alternatively, I suggest to normalize both scales to the average coffee consume of each country, double log the plot, and see whether it correlates with the local climate change impact.

  • Count Iblis

    I agree with B #42.

    I think that more scientists should go into politics, clearly politics is much too hard for politicians :)

  • Jonathan Vos Post

    Economics is indeed a science.

    My comments as a Fortune 100 employee and taxpayer are on the Good Math, Bad Math scienceblog.

    My comments as a published Mathematical Economist are as follows.

    Economics is indeed a science, at least since its first great quantitative book defining the key variables:
    Smith, Adam. An Inquiry into the Nature and Causes of the Wealth of Nations, 1776.

    Economics uses (and abuses) Math. In recent decades, LOTS of math. In serious imitation of and envy of Physics. I’ll skip the sidebar on whether “Econophysics” is or is not a valid approach, except to admit that I admire the best work of the Santa Fe Institute, and go on the record here in predicting a “Nobel Prize” in Economics to one or more at that venue.

    John Forbes Nash, Jr., is the Albert Einstein of Economics. Based on my breakfasts and lunches with him and his family, and the new work he’s doing, he is still doing important research. The Nash Equilibrium thesis that he wrote is one of the great results of the 20th century, far more reobust than he could have imagined, applicable in the context of, for example, Quantum Computing and entangled players.

    I have a few refereed papers in the field, mostly with senior author prof. Philip V. Fellman, which can be found (for instance) on the arXiv recently.

    The Wall Street Journal is not a refereed scientific journal. They have recently made fools of themselves. I regret that I could not have refereed that article and graph.

    But don’t throw the baby out with the very biocontaminated bathwater.

    Mathematical Physicists have managed to earn as much as $1.3 x 10^9 last year, to cite the conspicuous outlier.

    Just as Astrophysics equations suddenly got repurposed in Mathematical Population Biology when I was in grad school (1970s) so are Critical Phenomena, power laws, wavelets, differential equations (cf Black-Scholes), asymptotics of random graphs, and subtle analysis of 100s of gigabytes of time series data being used right now in studying actual markets.

  • Arun

    Habyarimana wrote:

    And if the people in country R want to hack a minority group to pieces, the thing to do is to use machetes.

    What you are suggesting is that we ought to rip off the rich in order to buy the votes of the poor. Dear B: you are in the wrong field. You ought to be a politician.

    Just who is it that opposes the reduction of the agricultural subsidies in the United States and Europe that are ripping off taxpayers in those countries and depressing the incomes of farmers in third world countries? (Hint – large corporations).

    Which two industries have seen both the most US government subsidies and tax breaks and record profits in the last 6 years? Defense and oil.

    It is the f***ing rich who are the most willing and most able to feed off the public trough. It is the whole juvenile ideology that the Habyarimanas of this world spout that keeps anything effective from being done about it.

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  • Solipsist


    thanks for once again confirming my prejudices about economists… (sorry! really trying hard to get rid of them, but mostly unsuccessful)

    are prejudices part of the phenomenologists’ doctrine ?

  • Tom

    Clearly we should just raise taxes to INFINITE. Clearly that would provide INFINITE income for everybody ! Just look at your curve ! Call washington, we have found the solution to all their income problems !


    Obviously the graph will hit zero at some point of taxation (because obviously at a tax rate of 101% the graph will hit zero within a year or so). And clearly 0% tax generates 0% GDP income from tax.

    So the curve CANNOT be linear. It has to be at least second degree. Or third. Dunno what will fit best. But it seems to me the economist is much closer on the money than you are.

    And btw, I’m a mathematician.

  • Philip Walker

    Discount Norway as a statistical outlier for the moment. The UAE stays, because it is empirical proof (as if such were needed!) that governments which don’t levy taxes don’t get money. Now look at Ireland, Luxembourg, Australia, France and the US, and tell me if they (and the others which are unlabelled) don’t form a beautiful Laffer curve, dropping quite steeply at about 35%. The Laffer curve is the maximum theoretical tax revenue, note, so it’s the boundary of the region of taxation.

    Interestingly, the data suggest that my own country, the UK, needs to focus not on changing tax rates (which look like they’re just under the peak) but on improving tax-collection efficiency (which moves us up towards the peak without sacrificing significant portions of domestic product).

    The danger of producing such rotten arguments in favour of your position is that people spot them as such, and mistake “bad argument” for “no argument”. They then conclude that your position is fundamentally flawed, and you succeed in winning critical thinkers for the opposition.

  • lamin

    Well, yes: Link

  • Neil B.

    Philip Walker,

    Good point. Way too many people fall prey to the fallacy of reversal, where an argument with some flaw is assumed to have no merit at all. They sometimes apply this to “crank” ideas. In this case, I agree that the really important thing (for our understanding, but it is still important to flag bad presentations) is not the hokey high-peaked curve, but the rough clustering between 15-35% rates, which could thus ideally be considered a “reasonable range” for liberal democracies that want to raise “adequate” revenue without oppressing business. However, the real trick here is that so many companies pay less, or are even given net payments, due to loopholes and lobbied rigging of the tax code. The percent figures, as a practical matter, are therefore dubious to begin with.

  • Biff

    It’s certainly easy to poke fun at other disciplines, especially those that are a little removed from one’s own.

    I was going to write some cogent argument pointing out that Economics is viewed as the dismal science, not because its practioners are charlatans, but because it is so hard. First principles are a little tricky to pin down… But in the light of this sort of ‘analysis’ (the graph) I probably better not bother.

    I’m not quite convinced by Brian’s (39) argument that business would continue under a 100% tax regime. I can’t imagine many of them would bother…

    I supose that every field has it’s unfair share of contributions from people with little knowledge of the subject but a powerful urge to talk about it anyway. Physicists and astronomers have IDer’s, nutjobs with perpetual motion machines and economists have everyone that knows the world would be a better place if everyone was more left/right wing.

    I’m glad I’m a software engineer. Everyone likes us. Or something.

  • silvermine

    It’s sort of amusing that in a post where you’re ridiculing someone’s ability to fit a curve, you make the classic blunder of assuming a linear fit is appropriate without any justification. Both plots are obviously ridiculous.

  • Sean

    Isn’t it amusing, though? Here’s the thing: the first plot was not a “fit” to the data, it was just a way of indicating the perfectly obvious fact that there seems to be a general upward slope in these data. Nobody claimed that the curve would never turn over, or that these things were the right axes to be plotting, or that higher taxes are always better. Any suspicion that those things were being claimed is more reflective of your inner mental state than any point I or anyone else was making using these curves.

    The point is that the AEI/WSJ curve was laughably ridiculous. A decent supply-sider could argue “Wow, that particular curve is egregiously bad, and they should be embarrassed; but a better analysis, with more appropriate data, would nevertheless show a turnover.” Such a person, whether right or wrong, would be “honest.” The actual people who seem to be showing up here are choosing instead to ignore the ridiculousness of the published curve (the point of this post), and to make fun of straw men that they are choosing to construct. That’s what we call a “hack.”

  • Tom

    Don (#34), thanks for making my point.

  • Tom

    Brian (#39), what if the tax rate is 110%? 200%? Do you think there is a point along this curve where tax revenue declines? I do (far below 100%, at a guess).

    The higher the tax rate, the greater the incentive to plan your taxes carefully. Even for whatever companies would remain under a 100% regime, presumably few accounts would show a net profit, and even fewer a substantial one.

  • Barry

    AJ on Jul 14th, 2007 at 9:19 am

    “Did anyone bother to look up the fact that this line is not being fit to the data?”

    It’s just there for decoration?

    “It is merely a curve which indicates ‘good’ ratios are below the curve and ‘bad’ ratios are outiside the curve.”

    Um, could you repeat that, in a way which makes more sense?

  • sesenta y cuatro


    Great job! It seems that someone actually wanted to discredit Laffer curve and could not find a better way to do it than manipulating these data.

    Who’s worst? Economists doing science or scientist doing business? I wonder

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  • blah

    Take UAE and Norway out as outliers, what is the confidence level of there being a correlation? Looks like random scatter to me.

  • Michael D

    An interesting point made over at Crooked timber with regards Norway as an outlier.

    In science, outliers are often easy to dismiss as measurement error, equipment etc. But how can you ignore a REAL country with REAL people?

    so you reply well they’ve got oil etc. so we just can. so what about all the other countries with oil or special ‘resources’ or exceptional state of affairs?

    read here for more:


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  • Ray Ladbury

    OK. Does anyone have the original data, because this one is just begging for a treatment with Akaike Information Criterion. You have a bunch of very noisy data, a simple model (linear trend) and a (very, very) complicated model that looks almost, but not quite parabolic–maybe a weibull of some sort. I’d bet the linear trend kicks serious tuckus.


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About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] .


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