The Tabarrok Curve in the WSJ

Matt Ridley covers patents and the Tabarrok Curve in the WSJ:

The economist Arthur Laffer is reputed to have drawn his famous curve—showing that beyond a certain point higher taxes generate lower revenue—on a paper napkin at a dinner with Dick Cheney and Donald Rumsfeld in the Washington Hotel in 1974.

Another economist, Alex Tabarrok of George Mason University, last year drew a similar curve on a virtual napkin to argue that, beyond a certain point, greater protection for intellectual property causes less innovation. He thinks that U.S. patent law is well beyond that optimal point.

Last week the Supreme Court came out against the patenting of genes, on the grounds that they are discoveries, not inventions, though it did allow that edited copies of the DNA of a breast cancer gene should be seen as invented diagnostic tools. Dr. Tabarrok thinks that decision and other recent rulings are nudging patent law back in the right direction after a protectionist drift in the 1980s and ’90s.

Jude Wanniski and the Wall Street Journal made the Laffer curve famous so I have high hopes!


And to think most people considered the laughable curve of Laffer's to be hilarious after the Reaganomics era, and a fine demonstration of how hopelessly economics became co-opted by ideology, especially on the supply side (also known as voodoo economics by a former Republican Party chairman, who later became president).

And one wonders - does the Tabarrok Curve have such an illustrious naming story? - 'The term "Laffer curve" was reportedly coined by Jude Wanniski (a writer for The Wall Street Journal) after a 1974 dinner meeting at the Two Continents Restaurant in the Washington Hotel with Arthur Laffer, Wanniski, Dick Cheney, Donald Rumsfeld, and his deputy press secretary Grace-Marie Arnett.'

One further hopes the Tabarrok Curve won't be condemned by one of its major paid proponents, the way Laffer's was - 'David Stockman, Ronald Reagan's budget director during his first administration and one of the early proponents of supply-side economics, was concerned that the administration did not pay enough attention to cutting government spending. He maintained that the Laffer curve was not to be taken literally — at least not in the economic environment of the 1980s United States. In The Triumph of Politics, he writes: "[T]he whole California gang had taken [the Laffer curve] literally (and primitively). The way they talked, they seemed to expect that once the supply-side tax cut was in effect, additional revenue would start to fall, manna-like, from the heavens. Since January, I had been explaining that there is no literal Laffer curve."'

So higher taxes have no effect on the economy then. Is that what you are saying?

The northern democracies who have weathered this crisis better than most learned a few decades ago that the Laffer curve was very real. They would increase taxes and get less revenue. A real problem if you are at the limit of your borrowing capacity. These governments have had to reform, something silly really, if they wanted to provide more services they had to be more efficient in using the resources they had. Once the lesson was learned the problem was, as you describe, to restrain politicians from spending the money that they imagined would materialize magically. The problem is spending. If your goal is to maintain current spending levels with growth from population or other natural growth factors, and you need to stop borrowing, the Laffer curve is very real. There is an optimum where revenues are maximized. But there never will be enough money for every politician's wet dream.

The curve is real. People don't actually look at it though: Many people just read it as if it meant that raising taxes lowers revenue, when that's only the case on part of the curve, not the entire thing.

Not every country is in the rightmost part of the curve. The trick is to figure out where you are.

I don't think any economist denies the Laffer curve. It's the later claim that tax reductions would always pay for themselves that was wrong.

I dont think any economist knows where on the curve revenues start to drop.


Research on the effect of changes in the marginal tax rate indicate that it is about 70%

Again with the fixation on 'tipping point'. The larger point of the Laffer curve is the declining slope all the way along. Is this not obviously true from economic theory?

This insight contrasts with the simple tinker-toy model: assume an economy of $X. Taxes = $X times tax rate.

Brian, any standard theory course will begin with a model of agents who maximize utility under an income-based budget constraint and face a labor-leisure trade-off. Once you introduce a marginal income tax, you can use the model to show how this affects the decisions to work and to consume. This is standard economics and Arthur Laffer did not contribute anything to the understanding here. You can derive the relationship between τ and τ*wage*hours worked -- the so-called "Laffer curve" -- by solving the model for hours worked and then using algebra.

If you think this relationship will have a "declining slope all the way along", you are unfamiliar with both economic theory and even with the point Arthur Laffer was trying to make. Like many models, this one is sensitive to parameter values and evidence (Piketty, Saez and Stantcheva) suggests the derivative of revenues with respect to marginal rates on high incomes in the U.S. is positive until about 70%.

Certainly none of Reagan's economists said at the time that the tax cuts would pay for themselves.

It's fascinating how both Democrats and Republicans are both convinced (for different reasons) that they did, though.

Maybe they should look up the Neo-Laffer curve then, because the Laffer curve is nothing but an arbitrary assumption created post-hoc to justify a pre-existing belief.

Are you unaware that the Laffer curve is a trivial consequence of elementary calculus? So you're declaring war on calculus?

Math creationism. Hm.

Are you unaware that data matters when estimating parameters? So you're declaring a war on empiricism?

Oh, and do you really think it's just simple calculus? Is it at all conceivable that the curve might look different under different economic conditions? And as matter of mathematics, maybe you could define for me what precisely this "tax rate" is?

The problem is everyone took the illustration too literally. Laffer's point was that when the tax rate is 0, revenue is also 0. When the tax rate is 100%, the revenue is 0. In between, it goes up, levels off, and comes down. That was it.

But people saw a nice, softly-sloping curve that looked roughly symmetric and thought that meant something. You could draw a billion version of "the Laffer curve" and none would necessarily be wrong. The problem is the roughly bell-shaped thing that people think of seems to indicate that cutting taxes will often generate revenue or at least not lose much. But there's no way that's what the actual curve looks like. Probably not even close. But it's nearly impossible to estimate empirically on a national scale, so Laffer's little bell is what people think of rather than a convex hill that eventually plateaus before cratering.

I think this is clearly true. However, there is a factor beyond "patent strength" that is very important in either encouraging or discouraging innovation.

Patents are supposed to be issued only for "novel" inventions. The formal definition of the term is given as "not obvious to one skilled in the art." Novelty or obviousness are certainly subjective judgements. How high one sets the bar for novelty can have enormous impact on the functioning of the patent system.

In the past 20 or 30 years, there have been many patents issued where the bar for novelty was clearly set very, very low. I think there are a combination of pressures behind this, but certainly major cause is the asymmetry between the huge and well-resourced patent departments in multinational companies on one side, and very under-resourced and generally inexperienced patent examiners on the other. Its not only resources, but also very asymmetric incentives between the sides.

Yes. This is an important point. The incentives for the examiners lean heavily towards issuing patents. One of the many insanities of the US patent system is that the only way to get rid of a persistent applicant is to give him a patent (because they can keep filing continuation applications).

Perhaps the patent examiners should be required to issue a letter grade for a patent's innovation/novelty. Patents that just barely clear the bar would be D, while something really new and clever would be an A. It wouldn't affect the legal standing of an issued patent, but it might sway decisions in patent litigation.

It would be even better if the letter grade translated to patent duration. "A", and you get 17 years (or 20 or whatever it is now). Get a "B", and you only get 12. Say 7 years for a "C" and 2 for a "D". There is actually a whole continuum between "obvious" and "non-obvious", it would be nice if our patent system recognized that.

That would change the privileges of owning a patent, as well as taking us further away from the international practice. My suggestion would not change the rights of a patent holder at all. It would just be sort of an advisory or criticism.

While I think it is probably a good illustration, it's so easy in Economics to come up with an elegant mental model which seems so tempting, natural and obvious but is unfortunately totally empirically false.

So, do we have any way to quantify this curve? Any quantitative surrogates for "Patent Strength" & "Innovation"? It'd be nice to see some actual data points. From the US / elsewhere and perhaps at different points in time.

For now it's an elegant fitted curve drawn before the points to fit it to were collected.

> For now it’s an elegant fitted curve drawn before the points to fit it to were collected.

This is a more than fair criticism. Hard data would be great. But consider how hard it is to quantify the benefits of patents. I'd have a hard time crediting a paper that claimed to compare different countries (or different eras in a country) and control for everything else except patent policy.

All I know is, in 2011, both Apple and Google spent more on patent litigation and defensive patent acquisition than on research and development. That kind of activity costs the smartphone industry $10 billion/year (about equal to Google's net profits, though of course Google is just one player in that industry and their profits aren't from phones). A BU paper estimated the "direct" cost of patent trolling at $29 billion in 2011—but note the word "direct" there. I think the authors are lawyers, not economists. They did not try to include the opportunity cost we're paying by having the country's most innovative people fight rent-seeking lawsuits instead of doing productive work, with massive positive externalities, that no one else can do.

Doug Crockford tells some stories, and recommends that the patent office be directed to review and deny all software patents. video

I think we are little further down the curve than indicated -- Innovation is currently below zero patent strength.

A one dimensional curve for IP (when complex products involve multiple patents), much less an x and y axis that are non-objective and undefined, doesn't make much sense as an objective measure, but it does for talking points, if you are the one who holds the chalk.

Ask yourself this question:

Are you supposed to call a 1-800 number every year to ask Alex where we are on the curve for that year.

Give it a good "sexy" name. I offer you the "Tabarrok Twist" and waive my IPR on it. Once it and you become famous, though, I'll expect you to credit me and lavish me with praise.

"Tabarrok's Tent"!

Tabarrok's Illusion.

There is no empirical evidence for such a relationship (Boldrin, Correa, Levine & Ornaghi, 2011). Optimal level of patent protection is zero.

In software, no doubt. Most companies wouldn't bat an eyelash, the consumer would not see a decrease in output, and the losers would be the lawyers. In biotech or pharma? I'd expect privately-funded research to pretty much disappear.

I find the use of the word "protectionist" to be disingenuous.

This is a place where a slightly "smarter" and edgier Michael Sandel is required.

The inflection is around 1980 on how to get rid of government policy.

On the justice of knowledge being a free good for all of humanity, it became how to make knowledge a free market good that generates private profit.

The solution was to change Federal law, and encourage State law changes so public institution obtain patents on discoveries, not inventions, but discoveries from basic research. Then the public institutions can sell its discoveries on the free market so the profit motive can fund basic research and government no longer controls the knowledge and taxes will be lower.

And in line with the other wacky theories of the time, the promise was privatizing previously public knowledge for profit, twice as much basic research would be bought by the profit seeking free market capitalists.

Basic research has fallen since, and while government spending as a share of GDP is smaller, it represents a larger share of both basic and applied research.

This is just another reason to vote for liberals because this is a wacky destructive idea from the right that comes out of the think tanks like Cato and Heritage and Hoover.

I remember when about 13-15 listening to my dad talk politics with old friends while we were on vacation, and it was very different than the message from the Weekly Reader version. And that's when public schools were teaching civics extolling equality and justice that led to all the 60s protests, fueling the long simmering backlash that defined all public institutions as leftist indoctrination factories, and all their activities as better done by private sector for profit monopolies. -- Today I have that "wisdom" my dad had because I lived through and lost the debates in the 80s to those who wanted to give me lower taxes, even though I explained how well off I was as a result of my dad paying "high taxes" for the "leftist indoctrination" that made me well off in the 80s.

Was it justice to not tax me, like my dad (and his dad) was willing to tax himself so the next generation would be better off? Why was I given a free lunch when I was willing and able to pay for the long leftist lunch I got decades before and was still enjoying?

My dad in the last years of his life getting treatment from cancer listed among his wonderful life all the change he had seen in his lifetime. He was the first in the family to buy a personal car, which led to the many miles of travel by car on Federal roads built initially to support the Post Office RFD Parcel Post innovation that the private sector could not accomplish in two centuries. The rise of commercial passenger air that led to his doing a lot of flying his father could never have imagined, a result of Federal government spending. Seeing the scifi he read as a young adult come true with the landing on the moon as a result of Federal spending. Color TV as culmination of Federal spending and mandates on AM radio, BW TV, public broadcasting, UHF mandates, FM mandates, color mandates, cell phones based on Federal research and mandates - he didn't live to see the DTV spending and mandates.

The US led in so many sectors coming into the 80s, but on exiting the 80s, the US was definitely falling behind, and we keep falling behind as the right wing keeps fighting the public investment in innovation by demanding more private ownership of knowledge and everything built from it.

+1 All you need to do is look at patent enforcement and protection before the 1980s to see that the innovative firms lost the protection of their patents because of patent hostility among the federal circuits.

Every heard of Xerox and the Xerox patents...ever heard of the copycats SCM and Cannon. Prior to 1981, the Antitrust Division had nine no-nos which, from an economic perspective, were indefensible for but a few. This also inhibited investment. Fortunately, patent antitrust policy changed in Republican and Democratic administrations.

Isn't ANY policy that's not uniformly bad going to have a strength-to-effectiveness curve that looks like that?

Policies could also be uniformely good, like for example copyright protection according to the RIAA.

One big difference to the Laffer curve is, of course, that while the Laffer curve is largely discredited (aka wrong)- but convenient for a fair number of vested interest groups, the IP protection curve is probably something that's likely right and that by now ~80% of economists believe, but that's rather inconvenient for a lot of vested interest groups. So from a political economy perspective I'm going to predict that the Tabarrok curve isn't going to go anywhere near the Laffer curve in terms of popularity. Anecdotal evidence no. 1 - I don't think anyone ever got fired from a GOP position for promoting views in-line with the Laffer curve, on the other hand:

The Laffer curve is not wrong, it has been discredited by politicians who use it to justify spending money that they haven't taxed. There is a limit at which revenues decrease when taxation increases. The question is where it is. There are countries who have hit the Laffer curve.

well, if you're going to be all precise about this - the original Laffer Curve had government revenue at 100% tax rate at 0, which is almost certainly wrong (people would.e.g. pay some taxes and move the rest of their activity off the book). I'm also not aware of any work that has actually demonstrated convincingly that any country has ever been to the right of the Laffer-curve's maximum. I think estimates for advanced developed countries are often around 70% - and that refers to the overall tax rate, not the marginal rate and no AIC has ever been there. The Laffer curve is also wrong in treating taxation uniformly, whereas in reality the tipping point is likely at very different points depending on the type of taxation.
So sure, if you want the Laffer curve to say that there is some level of overall income taxes - though one that has almost certainly never been reached in any advanced industrialized country - at which tax revenue decreases, it is correct. But that's not how it was originally drawn and it's certainly not how it was originally pitched by Laffer himself - it's not like he is or was some disinterested economist in an ivory tower...

? Another warrior against calculus.

The article's gated, ungated version on Ridley's blog:

Re: Laffer curve.

Yeah, I remember the enormous prosperity after tax cuts during two Cheney administration terms.

Let's hope Alex's curve has a more illustrious future than Art's.

How do you bait left-wing idiots into proving they are innumerate? Mention 'Laffer Curve' and watch them claim that it 'doesn't exist'.

Given that tax revenue is greater than $0 at rate 'R' they are denying at least one of the following:

A) Tax revenue when R = 0% is $0.
B) Tax revenue when R = 100% is $0.
C) One can use basic high-school calculus to prove that if A and B are true (plus the given state) the first derivative of tax revenue with respect to the tax rate must be both positive and negative at some point between R = (0%, 100%)

In my experience, the real problem is convincing right-wing idiots that the Laffer curve inflection point is not at zero.

This is one of the longest sequences of syntactically correct and internally consistent words that nevertheless conveys no information that I have read recently.

"some point," or "at least one point?"

And if we are dealing in abstractions, and giving math lessons, why can't the derivative be zero the whole way? Of course we know it's not, but that's empirical information, and cannot be proven using "high-school calculus," or any other kind.

And is the relationship between revenues and some mysteriously ill-defined variable called "tax rate" unchanging with respect to all othe variables?

Who's innumerate again?

@Jay PS, I think your grasp of calculus is a bit shaky. What's highly plausible (not axiomatically true) is that tax revenue is well approximated by a continuous function that increases until the rate of taxation chokes off work and investment and then decreases. Given that, the function will have a peak, quite plausibly a single peak at some point. Empirical research suggests that that peak occurs roughly at a 70% marginal tax rate on the highest incomes.

I don't know any lefty economist who denies the occurence of the peak, but there are certainly plenty of righty politicians who seem to think that the peak occurs near a zero percent tax rate.

The Y. Hsing model says around 32%.

Which is why tax revenues were so much higher after the Bush tax cuts.

Actually yes. Until the 2008 recession at least.

The bigger problem seems to be the uncertainty and inconsistency. Some concepts have patent proetction for a century or more, others have a commerical window as small as a year or two. And it seems like every important piece of IP is the source of endless litigation, which is only good for the legal/political classes. And the protection varies wildly from country to country, which creates arbitrage situations.

I just want to say I'm a huge Ridley-head so my already high regard for Alex just went up a couple more notches.

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