The Laffer Curve

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liveboy21
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The Laffer Curve

Postby liveboy21 » Wed Sep 19, 2012 12:21 am UTC

I want to discuss the Laffer Curve because it gets brought up sometimes when discussing economics and tax policies. I want to talk about whether you think the Laffer Curve is accurate and whether it has any significance to any ideologies.

I'll start by saying that I think that the Laffer Curve is a complete lie and is intended as a massive political misinformation strategy. I am of course willing to revisit this intepretation as more arguements are provided in this topic, which is why I'm creating this topic.

So, what is the Laffer Curve? (All information below will be taken from this wikipedia page) http://en.wikipedia.org/wiki/Laffer_curve

The Laffer Curve was an idea first publicised at a meeting with Arthur Laffer, Dick Cheney, Donald Rumsfeld and reporter Jude Wanniski. This curve was supposedly sketeched on a napkin to demonstrate their arguement against a tax increase.

The curve has 'Government Revenue' on the vertical axis and 'tax rate percentage' on the horizontal axis.

The basis is that if you tax 0%, the government will get no revenue. If you tax 100%, the government also not get revenue because people will not see a difference between working and not working (ie, people get paid nothing either way) and thus would all choose not to work. If you tax some number between 0% and 100%, government will get some revenue because people will be working and some of that money will go to the government.

Thus, they claim due to the mean value theorem, there must be at least one point between 0% and 100% which provides the maximum revenue. Inferring from that, they claim, if your tax rate is higher than this maximum point, a small decrease in taxes would actually increase the government revenue. Link to the mean value theorem here. http://en.wikipedia.org/wiki/Mean_value_theorem

So, that's their arguement. Why do I think that it's complete nonsense?

Mainly because their usage of the mean value theorem is completely wrong. Under the mean value theorem, the Laffer curve would need to be continuous between 0 and 100 percent. Unfortunately, because actual mathematics is not a good sales pitch, they neither show that this is the case nor do they even feel the need to claim that it is even necessary. Once you remove the condition of a continuous curve, the possibilities for the shape increase dramatically (though the original Laffer Curve shape is still possible, it is no longer the only possibility).

For example, without the need for a continuous function, there can be an increasing straight line between 0% and 100% but not including 100% and 100% would map to 0 Government Revenue.

So, taking some liberties with the math, the test for whether you think the Laffer Curve works is to think about 'What would happen if the tax rate werer 99%?' and if you wish to be more 'proper' with the math, you should think about whether the underlying assumptions in the curve make sense and whether it works with real world examples.

What are your thoughts?

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Re: The Laffer Curve

Postby rolo91 » Wed Sep 19, 2012 1:27 am UTC

I think that the conclusion that the Laffer curve argument is wrong, because of what you already said: Once you have a percentage lower than 100%, then working will ALWAYS be better than not working, as there are going to be benefits. People will try to improve their quality of life even if the increase is smaller.


But the conclusion can be still be correct, even if that argument is wrong: Decreasing taxes can lead to the government obtaining more benefits.

As an example, in my country (Spain) the opposite is happening: The government is trying to fix the debt crisis by rising taxes. As a result, people have less money to spend and the cost of products becomes higher. That means that people will spend less money, and without the money flowing, the state receives less indirect taxes, as there are less transactions to tax. So, they raise taxes, but end up receiving less money (and making the people more miserable).

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Re: The Laffer Curve

Postby jseah » Wed Sep 19, 2012 1:54 am UTC

What do I think will happen if the tax was 99%?
Uh... Bad Things happen?

Well, I think it is essentially the same as the 100% case. If I earned one cent for every dollar, I'll have to work for more than 24 hours a day to earn a living wage. Since clearly I cannot live that way, some other method to get enough to eat would be required. (Crime is one way, emigration is another)
Of course, not being totally ignorant of how the economy works, I would simply go about my business and not declare my earnings and everyone else would do exactly the same. It's not like anyone would work for the tax agency when they can't earn enough to eat either. Or the police when no one can pay them due to no one collecting tax (any remaining police are also tax dodgers). Oh, could be a good time to buy a gun too (no one enforcing licenses and black marketeers don't care about tax so they're still open), 's about to get very shooty up in here; maybe try to find a job/be a henchman with a big corporation/local warlord who can afford to run like a mafia and take care of their own.
... Oh, probably want to demand payment in foreign currency, cash. Or perhaps in barterable goods. This is economic meltdown scenario here.

Which would you choose: Don't pay your tax and maybe go to jail (who runs the jails anyway?); or pay your 99% tax and starve?
Either way, I'd be actively (more like desperately) trying to curry favour with the big boys so I can get out of the country.
Either way, the government gets as close to 0 tax as makes no difference.

And if the 99% tax was somehow magically enforced, I would buy the first plane ticket out of the country (sell everything, barter, beg/borrow/steal) because very soon there will no bread on the shelves and no planes to get out of there. I am not likely to succeed since I am not rich, but I'll damned well try my best because there sure isn't going to be many people around for much longer. One way or another.


- If this was a genie imposed tax, ala the Tuesday what-ifs, I would demand a pay rise of 100x. And the government would pay me or I'll be gone. And I'll be gone ASAP anyway; I'll probably go away rather sooner if they didn't pay me, you know, by way of not remaining in this world.
What this amounts to is a 99% communist, 1% capitalist economic system. After all, what this means is that 99% of economic activity is stuck in the government, so the government had better do 99% of the things the country needs to survive or the country will not.

-----------------------------------------

Ok, more seriously, you're probably talking about 99% tax bracket or 100% tax bracket at the top level of income. That won't cause an economic meltdown, and I'd be fine working in such a country (but definitely keep an eye out to move somewhere else; more effort would be put in the closer I get to the bracket), but if I had to start a family? No way, I'm getting out of dodge if I'm married with children.

I do not believe a long term 100% (or effective 100%) tax will do a country any good and raising a kid in a country about to go down the drain? Pfft, you couldn't pay me enough, literally, since the government takes it all away. Pay me tax free and I'll put the money towards buying my children an education (and hopefully citizenship) overseas.

And yes, the government will get nearly 0 tax from that bracket. Oh, there'll be a bit of payment at the start as people don't adjust instantly, but then they very soon have no money or find loopholes to dodge it.
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Re: The Laffer Curve

Postby Silknor » Wed Sep 19, 2012 1:59 am UTC

Is there a good reason to think it wouldn't be continuous?

Regardless, as a matter of public policy, the Laffer Curve is really only relevant if we're on the wrong side of it, or a tax increase would put us there. That's what proponents have had a hard time proving. For example, CBO analysis shows that the Bush Tax Cuts cost revenue. As did their 2-year extension. As did the cut in the payroll tax, the Making Work Pay Tax Credit, and every other recent tax cut or extension of a tax cut I can think of*. And their projections show a loss of revenue as well if the Bush Tax Cuts are partly/fully are renewed as compared to full expiration (the impacts on growth are more ambiguous, they see the cuts, partial or full, being good for growth in the short run, but bad for growth in the long run [5-10 years] due to the increased deficit).

I've heard claims than an example of where a tax cut increased revenue over the long term was on capital gains/dividend taxes (and I'm not sure that it did anyway when it was cut in 2003). The problem there is that since compensation choices can shift dynamically in response to tax policy, revenue from the capital gains tax increasing after the rate is cut does not mean overall revenue went up (again, I don't know that revenue from capital gains in truth went up, but it's a useful example). If the cut causes some companies to pay employees with income subject to capital gains instead of the tax on wages, then you can increase the revenue from the capital gains tax while decreasing overall revenue. This is a problem with the naive application of the Laffer Curve to actual tax policy. The Laffer Curve is about a single tax rate across society. Taxing capital gains and dividends at 100% might 0 out revenue from that tax, but the overall effect on tax revenue is more complicated: companies that now pay in part using payments subject to capital gains or dividends would pay wages instead, which are taxed at a higher rate currently. (Though it would probably decrease revenue overall simply due to the impact on growth).

IGM asked 40 economists where we are on the Laffer Curve with respect to federal income tax rates. Not one thought a cut in those rates would increase revenue (though most thought it would either boost GDP or were uncertain about that). An NBER paper found that we're on the correct side for both labor and capital taxes, but that Sweden and Denmark are on the wrong side for capital taxes.

*They even find a repatriation holiday would reduce revenue in the long run because while it would bring in a surge now, companies would be even more likely to hold profits overseas while waiting for another holiday.

@rolo91: Laffer Curve proponents would agree with you that there are revenues at any level of taxation between 0 and 100% exclusive. Eg. in a society with a single 99% tax, they would predict at least some amount of revenue.
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Re: The Laffer Curve

Postby CorruptUser » Wed Sep 19, 2012 2:40 am UTC

rolo91 wrote:I think that the conclusion that the Laffer curve argument is wrong, because of what you already said: Once you have a percentage lower than 100%, then working will ALWAYS be better than not working, as there are going to be benefits. People will try to improve their quality of life even if the increase is smaller.


Leisure still has measurable benefits; the extra income from working the additional hours may not be as great as the value from having free time. Otherwise everyone would work 100 hour weeks.

The Laffer Curve gets incredibly weird in that it also depends heavily on how those taxes are spent, how welfare is set up, etc. We had a discussion in another thread, and the Welfare Trap is horrendous in the US; when including benefits, a single mother earning $29,000/yr gets more take-home pay than if she earned $69,000 a year. According to the following, a single mother earning $44,000/yr is even worse off than if she earned nothing at all.

Spoiler:
Image

(Thanks to Lutz for finding this first)


To me, such a welfare system that actively punishes people for earning more is one of the most destructive systems imaginable. It's practically designed to keep people permanently in poverty.

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Re: The Laffer Curve

Postby curtis95112 » Wed Sep 19, 2012 3:02 am UTC

Before I begin, let me say that this is the first time I have heard of the Laffer curve and that the information in this thread constitutes the whole of my knowledge on the Laffer Curve.

I am almost certain that the Laffer Curve is continuous, barring artificial oddities such as improperly made tax brackets. The problem I have with the Laffer Curve as stated is that it doesn't tell us anything substantial. Sure there's an optimal tax rate. That's trivially true. Nobody (within error bars) advocates a 100% tax. The problem is how to find the optimal rate. And I don't see how the curve helps here.

Unrelated tangent: I don't like the use of the mean value theorem here. I'd prefer to use the extreme value theorem. It feels the more natural choice to show the existence of a maximum. To show the existence of a maximum using the mean value theorem would take a couple more steps and would feel rather contrived.
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Re: The Laffer Curve

Postby LaserGuy » Wed Sep 19, 2012 3:36 am UTC

I think Silknor's analysis here is the most salient: The Laffer Curve is only relevant if you know which side of the boundary that you are on, or, preferably, its functional form. People seem to think that the Laffer Curve somehow implies that we should lower taxes. This is only true in the case where you are beyond the maximum--at this point, the Laffer curve certainly does imply that taxes should be lowered, as this will both increase government revenues and increase growth. But any time you're below the maximum--which, I think you'll find is pretty much always--lowering the tax rate will decrease government revenues.

Moreover, there is no reason to believe that the maximum point on the Laffer curve is in any way the optimal place for the economy. It may be better to have lower government revenues if it leads to better growth, for example.

Also, reality is a little more complicated:

Image

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Re: The Laffer Curve

Postby Derek » Wed Sep 19, 2012 3:41 am UTC

The Laffer Curve is obviously real, and as Curtis pointed out you don't need the mean value theorem to prove it (I had forgotten the name of the extreme value theorem, thanks for reminding me). But as Curtis also mentioned, the mere existence of the curve doesn't tell us where we are on it. I suspect the peak is at fairly large tax rates.

It's also basically impossible to measure there are too many confounding factors. And in the real world we don't have a simple two variable function from tax rate to revenue, we have a function of many different tax rates on different kinds of income and different income brackets. In fact, it would be most accurate to describe it as a function from a tax curve or set of tax curves to revenue, where a tax curve is itself a function from income to tax rate. This gives you a domain of 2^2^Alpeh null to find a maximum over (or 2^Aleph null if you limit yourself to continuous tax curves). Have fun.

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Re: The Laffer Curve

Postby jseah » Wed Sep 19, 2012 4:18 am UTC

To illustrate one of the forces that generate this curve is my response to the hyperbole of the 99% tax rate. You may note that many of my reactions were "get the heck of out the country".

I might like to point out that upon finding that the UK has a 50% top tax bracket rate, I was already considering going elsewhere, like Australia (until I find their top rate is near 50% too). Of course, I probably won't hit that bracket but high top brackets point to having high just-under-top brackets too and generally high taxes.
Of course, as a fresh graduate, with ambitions for a PhD, and having zero commitments or ties to anywhere really, my international mobility is more or less "I go wherever I find work; and speaks English and gives me a visa". So I fall into the category of the kind of people who will just up and leave if we don't like your tax rate (and can find work elsewhere, obviously).
If I had the choice of going from an RA position in Australia at 20k after tax to an equivalent position as an assitant at Leica in the UK with 25k after tax (accounting for advancement opportunities), what does it matter to me where I work? I have literally nothing but visa applications stopping me from getting up one day and moving out if a job offer comes.

Higher rates = emigration of the high earners. Not all of them will leave, but some will. And this reduces your tax receipts.
IIRC, there was a case of the Lois Vuitton guy trying to leave France due to tax...
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Re: The Laffer Curve

Postby sardia » Wed Sep 19, 2012 4:40 am UTC

jseah wrote:To illustrate one of the forces that generate this curve is my response to the hyperbole of the 99% tax rate. You may note that many of my reactions were "get the heck of out the country".

I might like to point out that upon finding that the UK has a 50% top tax bracket rate, I was already considering going elsewhere, like Australia (until I find their top rate is near 50% too). Of course, I probably won't hit that bracket but high top brackets point to having high just-under-top brackets too and generally high taxes.
Of course, as a fresh graduate, with ambitions for a PhD, and having zero commitments or ties to anywhere really, my international mobility is more or less "I go wherever I find work; and speaks English and gives me a visa". So I fall into the category of the kind of people who will just up and leave if we don't like your tax rate (and can find work elsewhere, obviously).
If I had the choice of going from an RA position in Australia at 20k after tax to an equivalent position as an assitant at Leica in the UK with 25k after tax (accounting for advancement opportunities), what does it matter to me where I work? I have literally nothing but visa applications stopping me from getting up one day and moving out if a job offer comes.

Higher rates = emigration of the high earners. Not all of them will leave, but some will. And this reduces your tax receipts.
IIRC, there was a case of the Lois Vuitton guy trying to leave France due to tax...

I'm surprised you aren't calculating what benefits the government will provide you and only thinking about taxes in general. In addition, you probably aren't thinking about how various local taxes affect you. For example, that brazilian facebook founder ran to Singapore so he could avoid taxes on his facebook billions. However, a grad like you wouldn't go there unless you wanted to take advantage of the low technology startup taxes. This is in addition to changing citizenship, since the US will tax you for work done in other countries.

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Re: The Laffer Curve

Postby Derek » Wed Sep 19, 2012 6:19 am UTC

sardia wrote:I'm surprised you aren't calculating what benefits the government will provide you and only thinking about taxes in general. In addition, you probably aren't thinking about how various local taxes affect you. For example, that brazilian facebook founder ran to Singapore so he could avoid taxes on his facebook billions. However, a grad like you wouldn't go there unless you wanted to take advantage of the low technology startup taxes. This is in addition to changing citizenship, since the US will tax you for work done in other countries.

If he is likely to be in the highest or second highest tax bracket, he is not likely to be gaining much from government benefits.

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Re: The Laffer Curve

Postby firechicago » Wed Sep 19, 2012 11:28 am UTC

The Laffer Curve is a trivially true insight deployed in a dishonest way to support a false argument. Given that revenue at both a 0% and 100% tax rate will be zero, and that it is non zero at other rates, it must be true that there is a maximum revenue-generating tax rate, and that it is possible for a tax increase to reduce revenue and for a tax cut to increase it.

Where that tax rate is is an empirical question which is enormously complicated, but anti-tax crusaders regularly trot out the Laffer curve to oppose any tax increase and support any cut, without ever actually making an argument that this particular tax change will increase or reduce revenue. It's gotten so bad that you have politicians running around arguing that tax cuts almost always increase revenue, which is just silly.

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Re: The Laffer Curve

Postby curtis95112 » Wed Sep 19, 2012 12:39 pm UTC

I am inclined to agree. I see little merit to the curve. I mean, it would be useful if we had a good idea of what the curve looked like, but the only thing people seem to agree on is its value at the two extremes. Hell, even that's disputed. Just seems to be a lot of vacuous mathy-sounding crap.

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Re: The Laffer Curve

Postby Tyndmyr » Wed Sep 19, 2012 1:25 pm UTC

liveboy21 wrote:I want to discuss the Laffer Curve because it gets brought up sometimes when discussing economics and tax policies. I want to talk about whether you think the Laffer Curve is accurate and whether it has any significance to any ideologies.

I'll start by saying that I think that the Laffer Curve is a complete lie and is intended as a massive political misinformation strategy. I am of course willing to revisit this intepretation as more arguements are provided in this topic, which is why I'm creating this topic.


I think it exists. As a trivial demonstration of the upper bounds, a 100% taxation rate with perfect enforcement would result in no economy whatsoever. So yes, there is a point in taxation where increasing the taxation rate decreases overall revenues.

However, I think the point on the Laffer Curve we are at is...rather a lot below that point. This was actually something we explored in one of my macroecon classes...Reagan's folks theorized they were above the break-even point, but upon crunching the numbers...we got about a 6% return, well short of 100%+. So, decreasing tax rates did indeed stimulate the economy, but not nearly enough to make up for the lost revenue. Tax breaks are a useful tool, but not a budget panacea.

The same appears to be true of the current republican candidates. I can find no way to explain their budgetary errors but to assume they're making the same mistake. Given that tax rates today are not dramatically different from where they are under Reagan, I would expect the outcome to be similar.

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Re: The Laffer Curve

Postby lutzj » Wed Sep 19, 2012 1:31 pm UTC

It's worth noting that the peak of the Laffer Curve is an absolute maximum for revenue, and not necessarily optimal. You get diminishing returns as you get closer and closer to the peak by definition. Since governments ostensibly want to increase well being rather than collect as much tax revenue as can be squeezed out of people, the ideal tax rate is probably somewhere below the Laffer Curve unless the state spends money extremely effectively.
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Re: The Laffer Curve

Postby Tyndmyr » Wed Sep 19, 2012 1:33 pm UTC

lutzj wrote:It's worth noting that the peak of the Laffer Curve is an absolute maximum for revenue, and not necessarily optimal. You get diminishing returns as you get closer and closer to the peak by definition. Since governments ostensibly want to increase well being rather than collect as much tax revenue as can be squeezed out of people, the ideal tax rate is probably somewhere below the Laffer Curve unless the state spends money extremely effectively.


This is also correct..."how much revenue the government collects" is certainly not the only important element of economics, but it is something you'd want to keep an eye on. Of course, you won't want to ever set the taxation rate above the break even point, but you might well want to set it well below the break even point.

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Re: The Laffer Curve

Postby jseah » Wed Sep 19, 2012 2:32 pm UTC

sardia wrote:I'm surprised you aren't calculating what benefits the government will provide you and only thinking about taxes in general. In addition, you probably aren't thinking about how various local taxes affect you. For example, that brazilian facebook founder ran to Singapore so he could avoid taxes on his facebook billions. However, a grad like you wouldn't go there unless you wanted to take advantage of the low technology startup taxes. This is in addition to changing citizenship, since the US will tax you for work done in other countries.

Well, actually, I studied in Singapore for 12 years, and due to some... extraneous factors, I will not be working in Singapore ever again (I don't want to go there, the government won't give me a working visa).

But that aside, Singapore is actually a pretty nice place to work in. Clean and efficient. Tax code is simple (you file online), laws are business friendly (-ish), bureaucracy is low. Excellent connectivity to Asian markets as well as Western; both in a logistical sense and a financial sense. Stable government and currency. 20% top tax bracket, 18% corporate tax (IIRC).
Healthcare is pretty ok too; most companies have health insurance that works pretty well (family coverage, since my father's insurance covers me until 21 IIRC)


Little welfare, lack of interesting history (nothing like UK or US at least), excellent or worst education system depending on your mileage. Raising a family there? I'll have to think about it (assuming the visa problem is not one)
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Re: The Laffer Curve

Postby induction » Wed Sep 19, 2012 2:41 pm UTC

The Laffer Curve seems to be a repackaging of the golden mean. They both point out that there is such a thing as too much and too little, but tell you nothing useful about the points in between.

In the mathematical pedantry department: Even if you assume a continuous curve (which pretty suspect considering the complexity of the system being modeled and the existence of cutoff points for various benefits and incentives), there is nothing preventing multiple local maxima or negative values.

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Re: The Laffer Curve

Postby pizzazz » Sat Sep 22, 2012 2:59 pm UTC

I don't buy the continuity objection. It seems to me that I can make the change in revenue as small as I want by picking a small enough change in tax rates.

A better critique would be to ask what the tax rate on the x-axis refers to. Are we taxing income? Land? Consumption? Different goods have different elasticities and so the Laffer Curve will be different based on where the tax is applied.

lutzj wrote:It's worth noting that the peak of the Laffer Curve is an absolute maximum for revenue, and not necessarily optimal. You get diminishing returns as you get closer and closer to the peak by definition. Since governments ostensibly want to increase well being rather than collect as much tax revenue as can be squeezed out of people, the ideal tax rate is probably somewhere below the Laffer Curve unless the state spends money extremely effectively.


Right. The Laffer curve is probably brought up as often as it is because if the argument held, it would stop in its tracks any revenue-generating tax (as opposed to taxes meant to modify behavior). But as was pointed out above, the US is almost certainly to the left of the maximum, although some of the other modern democracies are probably on the right (and keep in mind there is not just 1 Laffer curve--2 countries could have different rates and still be at their respective maximums).

It is important to keep the curve in mind if there's a good chance you're already on the right side, lest your politicians get you in a vicious cycle of taxing to get more revenue when you actually are getting less.

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Re: The Laffer Curve

Postby Silknor » Sat Sep 22, 2012 4:01 pm UTC

pizzazz wrote:A better critique would be to ask what the tax rate on the x-axis refers to. Are we taxing income? Land? Consumption? Different goods have different elasticities and so the Laffer Curve will be different based on where the tax is applied.


While the basic insight that increasing the tax rate beyond a certain point can reduce revenue can be applied to a wide range of taxes*, the curve itself seems to only directly apply to income taxes**. The assumption under a 100% rate for example is that there will be no revenue. To try to apply that to sales taxes, you could say a 100% rate means the tax is equal to the pre-tax price, in which case it's obvious that the revenue generated is not 0 as long as some can't avoid the tax. Of you could take that as a 100% rate inclusive of taxes, means the tax cost approaches 100% of the total cost, eg. an infinite amount. While trivially true in a sense that the government would not generate revenue under a infinite per-item tax, it's not really relevant to the point of the curve, which is about work incentives.

*Excise taxes are one example where this is easy to see. It seems likely that beyond some point, higher cigarette taxes would reduce revenue from that tax (and thus overall revenue, as most other goods are taxed at lower rates). It may well be politically infeasible to reach those rates of course. And as with other taxes aimed at altering behavior, society may choose to set a rate above the revenue maximizing one in order to achieve the goal of decreased consumption of that product. Another practical example, beyond the scope of the Laffer Curve, is general sales taxes when it is easy to make large purchases in another jurisdiction, eg. people in New York City shopping in New Jersey.

**Another simplification the curve makes is to talk about a single tax on income. The actual tax system is, of course, far more complex. It is indeed quite conceivable that a 100% rate on certain types of income leads to a higher tax revenue than some lower rate (though it is likely not to be the revenue maximizing rate). For instance, I believe at least some some businesses can organize as either entities that pay the corporate tax on their profits and then distribute dividends or pass through revenue to their owners, who pay the individual rate. Assume that's the only difference. If the individual rate is 35%, the corporate rate is 5%, and the dividend rate is 5%, you create a large incentive to structure companies to structure to pay dividends instead of treating income as a pass through. If you raised the corporate rate to 100%, and every business was able to organize as a pass-through instead, then they would do so and so the effective rate on corporate profits would increase from just under 10% to 35%. Revenue from the corporate tax declines, but overall revenues increase (of course, that wouldn't work in the real world as the marginal corporate rate and the rate on dividends are far higher than in the example, and there's plenty of other considerations).

You can see this in reverse in the argument that lowering the capital gains rate would boost revenue from that tax. If that increase comes in part from restructuring compensation so a larger share is taxed under the capital gains rate instead of the individual rate, then the impact on overall revenue is ambiguous even if it is assumed that the capital gains tax proceeds increase.
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Re: The Laffer Curve

Postby TheEconomist » Fri May 15, 2015 2:59 pm UTC

First of all, anyone who knows any basic calculus could tell you that the theorem that applies is not the Mean Value Theorem. It is rolle's Theorem:
if f(a)=f(b), then there must be some point,c , where f'(c)=0. In other words, since f(0%)=f(100%), there must be some point c, where f(c) is at a maximum.
THIS IS BASIC CALCULUS!!!!!!
Secondly, the curve MUST be continuous. To say that it is not continuous is to say that the graph showing tax revenues as a function of tax percentages is piecewise or a scatter plot. This is NOT the case.
Thirdly, the Laffer Effect has occurred multiple times in history. The Ford tax cuts, the Harding tax cuts, the Reagan Tax cuts, and the Kennedy tax cuts. In each of these situations, lowering the marginal tax rates led to higher tax revenues from at least one income tax bracket.
The important thing to understand about the Laffer curve is that every single tax bracket has an entirely different graph with a different optimal percentage.

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Re: The Laffer Curve

Postby ahammel » Sat May 23, 2015 2:54 am UTC

TheEconomist wrote:Secondly, the curve MUST be continuous. To say that it is not continuous is to say that the graph showing tax revenues as a function of tax percentages is piecewise or a scatter plot. This is NOT the case.
This is not immediately obvious to me.
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Re: The Laffer Curve

Postby CorruptUser » Sat May 23, 2015 3:05 am UTC

ahammel wrote:
TheEconomist wrote:Secondly, the curve MUST be continuous. To say that it is not continuous is to say that the graph showing tax revenues as a function of tax percentages is piecewise or a scatter plot. This is NOT the case.
This is not immediately obvious to me.


To reiterate, Real Life does NOT hold up to what you learn in school. What mathematical distribution would you use to predict electric prices? That is for example, on a day a year from now, the price of electricity will be expected to be lognormally distributed with mean of $50 per MWh and volatility of 20. Were you aware that electric prices can be negative? That happens when too much electricity is produced (or a tree falls on a line), which can damage equipment so the plants have to shut down, BUT they take a few hours to start back up once shut so they are willing to be paid negative dollars just so they don't lose out during peak. And were you also aware that electric prices are never between $0 and $2? Because between $0 and$ 2, no one gives a shit, it just stays at $0. The math alone would never predict that.

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Re: The Laffer Curve

Postby Thesh » Sat May 23, 2015 5:19 am UTC

TheEconomist wrote: In other words, since f(0%)=f(100%)


That's not even a true statement.

Let's say I govern a community of people; they all farm, fish and make goods. I take all of those goods (100% taxation) and distribute them evenly among the people. People still work, since if they don't, there is no food, shelter, or clothing to distribute among them, and those are basic needs. Therefore at 100% taxation, tax revenue is greater than 0.
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Re: The Laffer Curve

Postby firechicago » Sat May 23, 2015 12:07 pm UTC

TheEconomist wrote:Thirdly, the Laffer Effect has occurred multiple times in history. The Ford tax cuts, the Harding tax cuts, the Reagan Tax cuts, and the Kennedy tax cuts. In each of these situations, lowering the marginal tax rates led to higher tax revenues from at least one income tax bracket.

The problem here is that it is impossible to disambiguate the effect of changes in marginal tax rates from the effect of the business cycle and other economic factors. Reagan cut taxes in 1981 and the economy grew. He raised tax rates in 1983 and the economy grew more. Then he cut taxes for high earners and raised them for low earners in 1986 and the economy kept growing. Then Bush left them the same and the economy crashed. So if you're going to make a claim about causality, like that "lowering the marginal tax rates led to higher tax revenues from at least one income tax bracket," you'd better have some way of separating the effects of tax rates from all of the million other things that are going on in the economy at any given moment.

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Re: The Laffer Curve

Postby BlackSails » Mon May 25, 2015 12:30 pm UTC

TheEconomist wrote:First of all, anyone who knows any basic calculus could tell you that the theorem that applies is not the Mean Value Theorem. It is rolle's Theorem:.


Rolles is just a special case of the mean value theorem

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Re: The Laffer Curve

Postby CorruptUser » Tue May 26, 2015 3:43 am UTC

Wow, it's like taking sophomore level classes in a subject doesn't mean you have a firm grasp of the subject.

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Re: The Laffer Curve

Postby Diadem » Tue May 26, 2015 9:56 am UTC

For Rolle's Theorem to apply in the first case, we need the function to be differentiable everywhere. That doesn't seem obvious to me at all.

Of course neither differentiability nor even continuity is necessary for the idea behind the Laffer curve to be correct. Sure we could have some non-continuous function that only has a supremum and not a maximum, but unless politicians habitually change taxes by ϵ, that doesn't really matter. It's still clear that tax revenue is not maximized at 100%, and that there must be a point where any significant change in tax rate will lower total revenue.

Of course the whole Laffer-curve argument still suffers three fatal flaws:
1) We have no idea where this maximum is, and no reason at all to think we are anywhere near it.
2) What a country does with its taxes is probably much more important then exactly how high these taxes are.
3) As others have pointed out, maximizing tax profit is obviously not the goal governing.
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Re: The Laffer Curve

Postby CorruptUser » Tue May 26, 2015 1:34 pm UTC

4) the Laffer curve may be different for different people.

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Re: The Laffer Curve

Postby leady » Tue May 26, 2015 2:00 pm UTC

on that example, the tax rate in the UK definitely stops me working more because I can choose to stop progressing and I don't see the point in working stupidly hard to see an effective 55% of any additional earnings go straight to the government (40% + NI + VAT )

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Re: The Laffer Curve

Postby elasto » Tue May 26, 2015 5:36 pm UTC

leady wrote:on that example, the tax rate in the UK definitely stops me working more because I can choose to stop progressing and I don't see the point in working stupidly hard to see an effective 55% of any additional earnings go straight to the government (40% + NI + VAT )

Which very neatly makes the point that raw revenue isn't the only goal of government.

All its citizens 'working stupidly hard' might be good for a country's GDP, but is it good for their health or quality of life?

If government policy wouldn't prevent you moving to a new job where you worked the same hours but for more money, but offers no incentive for you destroying your work-life balance by working a 60+ hour week, isn't that actually quite a healthy route to be encouraging you towards?

Peace of mind (through generous social safety nets should bad luck befall you), a healthy family life, vibrant leisure pursuits and so on - these are all just as valid goals of government policy as personal enrichment.

Noone lays on their death bed wishing they'd spent more time in the office, as the old saying goes. Instead of feeling sad that there's little point spending more hours working, go off bungie jumping or something instead :D

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Re: The Laffer Curve

Postby Tyndmyr » Tue May 26, 2015 8:01 pm UTC

elasto wrote:
leady wrote:on that example, the tax rate in the UK definitely stops me working more because I can choose to stop progressing and I don't see the point in working stupidly hard to see an effective 55% of any additional earnings go straight to the government (40% + NI + VAT )

Which very neatly makes the point that raw revenue isn't the only goal of government.

All its citizens 'working stupidly hard' might be good for a country's GDP, but is it good for their health or quality of life?


Exactly. Ideally, a government exists because it improves life for it's citizens. Citizens don't exist solely to improve the government.

So, while it's certainly the case that one or more points exists that optimize tax revenue, that alone isn't sufficient to determine that taxation should be set at one of those points. Or to determine which of those points it should be set at, if more than one exist.

Ideally, we would wish to measure tax rate against general welfare of the population. That's probably kind of hard and subjective, though. So, measuring against the economic success of the country is probably as good as we can reasonably hope to do. There's probably an ideal range of taxation and corresponding spending for a given country.

However, even with the simplified metric of GDP, we still have quite a lot of complication to determine the ideal taxation rate with any precision. For one thing, all possible spending options probably do not have equal results. Therefore, different governmental spending plans can be expected to cause holy hell with your measurements. Additionally, some effects on GDP AND governmental spending are external. Defense spending is going to be an area of some contention, of course. How do you determine the optimal amount for that in an objective fashion? Even if you can, it seems deeply unlikely to have a simple correspondance to GDP(or to tax reciepts).

The laffer curve is perhaps an interesting and useful conceptual tool, but it forms only one part of a very complex system. Still, assuming a nice, continuous curve, we can assume that maximal tax reciepts is a practical upper ceiling for taxation, as any taxation level that is sufficiently strong as to cause a decrease in the economy so large as to reduce tax reciepts overall is obviously undesirable.

But, that only gets you an upper bounds, not a lower bounds. And that upper bounds appears to be fairly high in absolute terms, so it's not THAT informative.

CorruptUser wrote:
ahammel wrote:
TheEconomist wrote:Secondly, the curve MUST be continuous. To say that it is not continuous is to say that the graph showing tax revenues as a function of tax percentages is piecewise or a scatter plot. This is NOT the case.
This is not immediately obvious to me.


To reiterate, Real Life does NOT hold up to what you learn in school. What mathematical distribution would you use to predict electric prices? That is for example, on a day a year from now, the price of electricity will be expected to be lognormally distributed with mean of $50 per MWh and volatility of 20. Were you aware that electric prices can be negative? That happens when too much electricity is produced (or a tree falls on a line), which can damage equipment so the plants have to shut down, BUT they take a few hours to start back up once shut so they are willing to be paid negative dollars just so they don't lose out during peak. And were you also aware that electric prices are never between $0 and $2? Because between $0 and$ 2, no one gives a shit, it just stays at $0. The math alone would never predict that.


Nah. Simple math alone would never predict that. Sufficiently complex math can simulate anything.

Economics, particularly macroeconomics, is field used to model a vast number of interactions. All the models are wrong, but some models are sufficiently accurate as to be useful. Mostly, we want models that are simple enough to actually use, while still accurate enough to give us mostly decent info.

So, it's not that we CANT model all manner of edge cases, simply that doing so generally doesn't yield enough additional accuracy to be worth the trouble.

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Re: The Laffer Curve

Postby mcd001 » Wed May 27, 2015 5:12 pm UTC

elasto wrote:Which very neatly makes the point that raw revenue isn't the only goal of government.

Revenue should not be a goal of government, ever, at all, in any circumstance. Yes, a government needs revenue to fund its legitimate purposes, but it should not seek revenue beyond that. I am disheartened by the number of U.S. voters (and the politicians they elect) who seem to believe that government policies should be designed and implemented to maximize revenue for an increasingly powerful government.

Not that the tax rate matters to the government; it just spends borrowed money to make up the difference. The U.S. federal debt (not including unfunded liabilities like social security) is currently over $18,000,000,000,000. Despite this, deficit spending continues without restraint, primarily because both political parties have embraced it. I believe this is unsustainable in the long run (even while I have no idea what the 'long run' is in years). Any politicians who actually think about such things have likely concluded they'll be gone before the day of reckoning arrives. They're probably right; I believe it's our kids who will pay the price for our fiscal irresponsibility.

On topic: while the Laffer Curve is a real thing, it is a completely useless tool for public policy because no one knows what it looks like. (Nor do I believe there is any way to accurately compute it for the incredibly complex real-world systems it is modeling.)

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Re: The Laffer Curve

Postby Tyndmyr » Wed May 27, 2015 5:20 pm UTC

mcd001 wrote:
elasto wrote:Which very neatly makes the point that raw revenue isn't the only goal of government.

Revenue should not be a goal of government, ever, at all, in any circumstance. Yes, a government needs revenue to fund its legitimate purposes, but it should not seek revenue beyond that. I am disheartened by the number of U.S. voters (and the politicians they elect) who seem to believe that government policies should be designed and implemented to maximize revenue for an increasingly powerful government.

Not that the tax rate matters to the government; it just spends borrowed money to make up the difference. The U.S. federal debt (not including unfunded liabilities like social security) is currently over $18,000,000,000,000. Despite this, deficit spending continues without restraint, primarily because both political parties have embraced it. I believe this is unsustainable in the long run (even while I have no idea what the 'long run' is in years). Any politicians who actually think about such things have likely concluded they'll be gone before the day of reckoning arrives. They're probably right; I believe it's our kids who will pay the price for our fiscal irresponsibility.

On topic: while the Laffer Curve is a real thing, it is a completely useless tool for public policy because no one knows what it looks like. (Nor do I believe there is any way to accurately compute it for the incredibly complex real-world systems it is modeling.)


Debt is tricky. Borrowing more and paying interest is possible, so long as the rate of borrowing does not grow exceedingly fast, and the rate of growth keeps ticking upward. But...growth is not perfectly constant. You have a recession and what do you do then? Stop borrowing and intensify the cash flow issues? In theory, perhaps, you could borrow in the bad times, and show restraint in the good, but that has a spotty historical past. People are just not particularly good at planning decades in the future, and even if you slap them together in groups and label them government, that problem remains.

It should be possible to determine the Laffer curve in real world scenarios. We can extrapolate from historical changes to the tax burden. If increases resulted in decreases in revenue, it'd be obvious that we were to the right of the optimal point on the curve(from a revenue optimization perspective). This does not seem to be the case. We seem to be well short of the maximal taxation point, so...determining the curve with some degree of accuracy is quite possible, but there's little reason to do so. It doesn't provide us much information that we can actually act on.

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Re: The Laffer Curve

Postby ucim » Wed May 27, 2015 6:22 pm UTC

Tyndmyr wrote:It should be possible to determine the Laffer curve in real world scenarios. We can extrapolate from historical changes to the tax burden. If increases resulted in decreases in revenue, it'd be obvious that we were to the right of the optimal point on the curve(from a revenue optimization perspective).
This only works if the curve is single-humped. If there are several local maxima, you're ch*rped using this technique.

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Re: The Laffer Curve

Postby Derek » Wed May 27, 2015 6:34 pm UTC

ucim wrote:This only works if the curve is single-humped. If there are several local maxima, you're ch*rped using this technique.

Jose

More significantly, it only works if you can control for every other economic factor. Have fun with that.

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Re: The Laffer Curve

Postby Tyndmyr » Wed May 27, 2015 7:38 pm UTC

ucim wrote:
Tyndmyr wrote:It should be possible to determine the Laffer curve in real world scenarios. We can extrapolate from historical changes to the tax burden. If increases resulted in decreases in revenue, it'd be obvious that we were to the right of the optimal point on the curve(from a revenue optimization perspective).
This only works if the curve is single-humped. If there are several local maxima, you're ch*rped using this technique.

Jose


Granted. But such a pattern should become fairly obvious if you're collecting data. Extremely high tax rates are fairly rare in practice, but do seem undesirable, and highly unusual tax rates do have a significant effect on production. Granted, much of this is extrapolation from smaller sample sizes, because raising the overall tax burden to approach 100% is normally not done. Presumably because of fear of the results.

Derek wrote:
ucim wrote:This only works if the curve is single-humped. If there are several local maxima, you're ch*rped using this technique.

Jose

More significantly, it only works if you can control for every other economic factor. Have fun with that.


This is a little harder, yes. In particular, it makes it very difficult to use data from other countries, since economic conditions are often very, very different. Looking at before and after of a tax change gets us a mostly decent comparison, but a degree of imprecision is inherent.

Still, I think it's safe saying that modern tax rates are generally not higher than that producing maximum government income, though they may be lower. The effect on the economy from tax increases/decreases is not nearly so severe as we would expect if we were past that point. A dramatic enough change would be obvious even with other effects at play. If there was some "tax rates above 10% kill the economy" effect at play, it'd be obvious in the data, and we just don't see that.

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Re: The Laffer Curve

Postby leady » Wed May 27, 2015 9:19 pm UTC

You have to also consider that the laffer curve is most regularly brought up with regards to the marginal rates of the highest levels of tax in a progressive system. There is a fair amount of data highlighting that approaching 50% yields little but better accountants (such as the cynical 50% top rate labour left in the UK as a poison pill - awesome politics, crap economics)

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Re: The Laffer Curve

Postby Tyndmyr » Thu May 28, 2015 12:27 pm UTC

leady wrote:You have to also consider that the laffer curve is most regularly brought up with regards to the marginal rates of the highest levels of tax in a progressive system. There is a fair amount of data highlighting that approaching 50% yields little but better accountants (such as the cynical 50% top rate labour left in the UK as a poison pill - awesome politics, crap economics)


That's fair. It's a somewhat different question from overall tax burden, but one would expect the same to apply to taxation on a given subset. The actual tipping point might not be the same in all instances, but it should still exist, and be a testable thing.

Tax avoidance* definitely seems to be strongly associated with richer/more heavily taxed folks, and that definitely does line up nicely with what we'd expect to see from incentives.

So, that's at least somewhat useful data, because very high tax rates for top income brackets do get proposed.

*In the legal sense, largely because tax evasion is somewhat harder to quantify accurately.

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Re: The Laffer Curve

Postby mcd001 » Thu May 28, 2015 9:04 pm UTC

Tyndmyr wrote:Tax avoidance* definitely seems to be strongly associated with richer/more heavily taxed folks

Probably because rich folks in the U.S. pay a disproportionate amount of U.S. income tax. (In 2011, the top 5% of income earners paid 56% of federal income tax, while the bottom 50% of earners paid 3%). There's no need to avoid or evade taxes that you're not paying.


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