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Taxing Top Incomes in a World of Ideas [pdf] (columbia.edu)
29 points by barry-cotter 71 days ago | hide | past | web | favorite | 63 comments



This paper considers the taxation of top incomes when the following conditions apply: (i) new ideas drive economic growth, (ii) the reward for creating a successful innovation is a top income, and (iii) innovation cannot be perfectly targeted by a separate research subsidy — think about the business methods of Walmart, the creation of Uber, or the “idea” of Amazon.com. These conditions lead to a new term in the Saez (2001) formula for the optimal top tax rate: by slowing the creation of the new ideas that drive aggregate GDP, top income taxation reduces everyone’s income, not just the income at the top. When the creation of ideas is the ultimate source of economic growth, this force sharply constrains both revenue-maximizing and welfare-maximizing top tax rates. For example, for extreme parameter values, maximizing the welfare of the middle class requires a negative top tax rate: the higher income that results from the subsidy to innovation more than makes up for the lost redistribution. More generally, the calibrated model suggests that incorporating ideas and economic growth cuts the optimal top marginal tax rate substantially relative to the basic Saez calculation.


There doesn't appear to be any empirical justification for anything the author has done here. Does anyone really believe that 1/ the "stock' of ideas can be measured by a real number and 2/ national output is proportional to some power of the "stock" of ideas?

Like, how do you even measure an idea? The paper feels like the author has done a load of maths and shoehorned one particular interpretation onto his equations.


That's exactly what he has done and there is nothing wrong with that when it's done right (Charles I. Jones is a top man).

>Does anyone really believe that 1/ the "stock' of ideas can be measured by a real number and 2/ national output is proportional to some power of the "stock" of ideas?

System dynamics can be modeled with numbers that can never be measured or are hard to measure. The exact number of working hours and capital spend to produce innovation is hard to measure and approximations (like what companies announce or number of patents) don't capture the whole picture. It's still reasonable to assume that the number exists.

Optimal taxation and economic growth are big subjects and this paper is not trying to solve it or propose a policy. The paper explores the dynamics of taxation and growth under three conditions mathematically ignoring the rest. Trying to see how big effects small changes can have is interesting.


> That's exactly what he has done and there is nothing wrong with that when it's done right (Charles I. Jones is a top man).

That sounds like an argument from authority to me. If he decides to use the form Y = A^b L and I decide to use, say, a confluent hypergeometric function, who's to say who is correct?


> who's to say who is correct?

Nobody. My friend studied econometry. I was appaled to hear that they just take some real process, assume it's governed by some equation then massage all the maths they can out of it.

They consider different equation for the same process (although they usually have favorite one) and never bother themselves with proving if any of them is actually reflected in reality of said process.

It's basically philosophy for people that can do some math.

They also use the math without deep understanding of it (sort of cargo cultishly). That I know because I worked for a prof and a post docs of econonometry on some project later.


> who's to say who is correct?

Someone who knows the economic growth theory better than I do. I have studied growth theory maybe 16-20 hours total. I'm not humble guy but I know I don't have the ability to join the debate and argue against. My hope is to learn the gist of the paper. In my comments I didn't try to argue for or against, I was trying to describe what the article is about.

Assuming that you are random guy in the internet who suffers from insomnia, I think your level of knowledge is even smaller than mine.

> If he decides to use the form Y = A^b L

That form is not his idea. It's very basic for all steady-state growth models. These models require strong assumptions like Cobb-Douglas production function, labor-augmenting technological growth and linear differential equation (only asymptotic requirement). To go trough all the assumptions would require a seminar.


Ok, let me try this again. Have you, (presumably) an economics student, ever seen an empirical justification for a Cobb-Douglas production function? Would I see such a justification if I opened, say, Mankiw's textbook?

If not, how do you know the assumptions are reasonable?


> Would I see such a justification if I opened, say, Mankiw's textbook?

Yes. Starting page 58. Cobb–Douglas was derived to match empirical observations (constant factor share, constant capital and labor share) and it was proved to have some nice properties.

Note that Cobb–Douglas only approximately true starting point. It does not capture everything. For example capital and labor shares are not completely constant. The simplicity of the function makes it useful and it's taught in basic econ. classes because it holds true well enough. You need slightly more complex models or relax the function for some stuff.


Ok, now we're getting somewhere. Mankiw says [0]:

Paul Douglas was a U.S. senator from Illinois from 1949 to 1966. In 1927, however, when he was still a professor of economics, he noticed a surprising fact: the division of national income between capital and labor had been roughly constant over a long period. In other words, as the economy grew more prosperous over time, the total income of workers and the total income of capital owners grew at almost exactly the same rate.

Douglas' evidence isn't actually presented in Mankiw, it's just stated as fact: do note that I asked for empirical evidence in my earlier post. The observations are over 90 years old, and the government didn't even collate national statistics in the 1920s. Do they still hold? Do they hold in non-US countries?

I'm not these modelling choices (cobb-douglas above, and the assumptions in TFA) are wrong, I'm saying that they're unjustified.

[0] http://irfanlal.yolasite.com/resources/N.%20Gregory%20Mankiw...


"by slowing the creation of the new ideas ... top income taxation ..."

Is this proven anywhere? I don't believe high taxation reduces innovation, in fact perhaps the opposite is true overall.


The paper assumes that innovation is incentivized by the "top" income received through it by the innovator. Under this assumption, since taxation reduces "top" income, it thus disincentivizes innovation.

The introduction further clarifies the author's definition of the type of innovation that gets disincentivized. "Basic research", i.e. innovations in our understanding of our world, are readily funded by the redistributed tax revenue. "Applied innovation", that which applies the outputs of basic research, includes the creation of Amazon.com or the latest improvements to Google search. This applied innovation is what gets disincentivized.

I personally agree with you that this is a shaky, unsubstantiated foundation for an argument about optimal tax policy.


My immediate question is what the innovators do instead of innovating when the tax rate is higher. Taxes reduce income, but they do so monotonically without affecting the relative ordering of options, which is what matters for income-maximizing decision making. The "top" income may be numerically lower, but it remains at the top.


The absolute values do matter. If Jeff Bezos expected Amazon to be much less profitable as it is for him, he may have decided to just stop and retire once it provided enough passive income to let him live comfortably. He would be paid more for the added time and stress of continuing to grow Amazon, as you say, but if that marginal income approaches zero, it just isn't worth it (and we are left without Amazon).


Since this is a claim asserted without basis (nobody can claim to know a counterfactual, let alone someone else's mind), I can also assert the opposite: Bezos didn't get to where he was without having a hell of a drive for success, and that drive is not 100% driven by monetary reward. Prestige, power, influence are all incentives built into us at the biological level, and if he gets to be the all powerful CEO of a $800B company instead of a $1T company, I don't imagine he'd throw in the towel.


I think you underestimate how much welth is used as a proxy to guage prestige, power, and influence amung the super rich.

People with drive don't do it to just be one of millions to reach a given milestone. People with real drive don't enjoy doing something that many before them have done.

Guys like Jeff clearly set out to be the best. Breaking the score bord could very well prevent something like Amazon, and we might have ended up knowing Jeff as the guy who has the largest POG collection.


Ok so he's a guy with insatiable drive, a hunger for success, a need to be the best- aw, hell, tax rates are a bit too high, why not throw in the towel?


No he would use the same talent to minimize taxes. Why would anyone expect otherwise lol ?


I think we need a movement that glorifies the payment of taxes.


I don't buy this, because we're not proposing to only tax Bezos until he has the exact same net worth as Joe Schmoe who collects POGs--this is a straw man. If we tax all the uber-rich 5% more, everyone would be in the exact same position on the leaderboard, just with slightly deflated numbers. We'd be having the conversation about breaking the $1T barrier 12 months down the line, BFD! It's just numbers to the rich, but it's life or death to the poor.

There's a story about a society of peacocks who grew their tails so big and beautiful it started interfering with survival. They'd get it stuck in branches, be too slow to run from predators, etc. No one peacock was willing defect and shorten his tail because he'd lose out on the mating game. If they could all just get together and agree to shorten their tails by 25%, they could keep the relative pecking order and also be agile enough to survive.


The problem with these game theory "let's just all work together" solutions is that they are not stable points. It is in everyone's best interest to undercut the cartel. Even if you did get all the peacocks to shorten their tail, if there is some advantage to having a larger tail, it is irrational to expect noone to try and grow it out again.


You don’t solve the prisoners dilemma by saying “fuck it let’s just all stab each other’s backs”. I’m arguing humanity should cooperate to achieve the better state, and punish defectors if needed to balance the incentives. This at least should be our aim.


Come on, I don't believe Bezos would put on his slippers and retire to a country cottage because tax rates were too high.

While money is certainly an incentive to innovate, it's also not the only incentive (and probably far down the list if you're already rich), and creative, driven people will do what they do whether or not a chunk of their "earnings" gets given/taken back to the society that enables them to do it.


True, but it's not just an incentive, it's also an enabler. SpaceX was on the verge of going broke, and their first successful launch was do or die. Had Musk been taxed more heavily before that, and had substantially less money to pour into the company, they likely would not have survived to make that launch.


But does Amazon provide a large net value? Google I can understand provides a service we didn't have, but amazon just provides "selling stuff" - something that was possible before too. If anything, Amazon now sells tons more stuff using a lot fewer jobs, so what is the net contribution Amazon does to the US economy in terms of job creation, tax revenue, and the Global ecnonomy?

If anything, a lot of the megacorps just seem to kill smaller business while at the same time being better at not paying taxes.


Whilst I sympathise with this view, it does ignore AWS and the value it provides to the businesses that use it, many of whom are SMEs/startups that might have struggled to get going otherwise.


Yes I was considering only Amazon the online store and its value compared to having multiple other/smaller stores - both physical and online.


Efficiency. By using Amazon I save time and can use the time saved to create something of value or to bill more hours or something else that will lead.to more tax revenue.


The net contribution is consumer surplus.


Even if that were true, would that have reduced innovation? How many other innovators has Amazon crushed—fueled by the “top income”?


Taxes may not affect the relative ordering of the (ex-post) outcome of the different options. But they can affect the relative ordering of the (ex-ante) expected value of the different options.


Applied innovation is risky requires investments into new devices, training, new logistic chains etc.

>Hall and Woodward (2010) provide a different perspective. Using an extensive data set on venture capital funding from 1987 until 2008, they show that the returns to entrepreneurs are extremely skewed: nearly 3/4ths of entrepreneurs receive nothing at exit, while a few receive more than a billion dollars. An entrepreneur with a coefficient of relative risk aversion of two values this lottery with a certainty equivalent of only slightly more than zero. An implication is that the tax rate that applies to the successful outcome can have a substantial influence on entrepreneurial activity.

I find it hard to see how taxation does not disincentivize applied innovation in the margin.


Even if innovation is motivated by top income we don't know how exactly they are related. For example if top income is taxed it's still top in relation to other income. With people usually relationships matter not the absolute values.

Also even if people work for a chance to be in "top" the probability of actually getting there might be irrelevant. People horribly overestimate probability of positive outcomes. Basiaclly 1 in a million and 1 in a billion is a the same for people. What's more they don't translate both to "impossible" but to "it's gonna be tough but I got a shot"


I think it could be reasonably argued that taxation, if not mismanaged, can actually increase net innovation by allowing more people the freedom, security, and education needed in order to be able to spend time innovating instead of surviving.

The whole reason the priesthood (and to an extent nobles too) was the core of education way back in medieval times was because they didn't have to worry about surviving. On the other hand, peasants could barely innovate at all because they spent most if not all of their time in labor.


I need these tax papers in docx format. Can I use PDF Converter for this? https://www.coolutils.com/TotalPDFConverter


People talk about how much they make pre tax. I think past a certain level of income, you gain the same status per marginal dollar and the actual additional purchasing power does not matter...


That is true, but the numbers are probably higher than you think. At least for me, I think wealth at least (as distinct from income) makes a non-trivial difference to me up until I can afford to live the rest of my life comfortably without continuing to work for someone else.

Now, above that level, there are actually some other emotionally satisfying wealth strata, such as:

- Ability to invest in or personally found/fund companies for ideas that you have

- Ability to found/fund charities that you think would make the world better

I'm not saying that everyone needs to achieve these things to be happy. But I would say that I think it's easy to look up to say, 2-3x your own income and say "how could anyone ever want more than that", but then when you get there, you find that actually there's a lot of interesting stuff that you might be able to do if you made 5-10x more still, and at least for me, it's mostly not about luxury. It's about being able to pursue interesting things with autonomy.


> I'm not saying that everyone needs to achieve these things to be happy. But I would say that I think it's easy to look up to say, 2-3x your own income and say "how could anyone ever want more than that", but then when you get there, you find that actually there's a lot of interesting stuff that you might be able to do if you made 5-10x more still, and at least for me, it's mostly not about luxury. It's about being able to pursue interesting things with autonomy.

This is called the hedonic treadmill and is pretty much built into all humans. Spoiler alert: it never ends.


Indeed it is. And on a personal level, that can be a tragedy. But on a social/economic level, it's great for raising everyone's living standards, which is the point of this paper.


> up until I can afford to live the rest of my life comfortably without continuing to work for someone else.

There are probably a few exceptions (i.e. 19 year old superstar athletes who just signed their first major league contract) but I would generally assume that when we're talking about people with annual income in the > $10MM range, then those people already have more than enough wealth to live comfortably forever without working.


Totally, but the point of this paper isn't the people who already have $10mm. It's the people who want to get there, and what they're willing to sacrifice to do it. Building a massive business like say, Amazon, takes enormous personal sacrifice and risk. The high incomes that result from it incentivize that sacrifice/risk. They cause the person who currently has relatively little, to risk what they do have to produce something great, something that we all benefit from.

The point of this paper is that there is an amount of risk/sacrifice people will make for $10mm, that is different from what they will make for $100mm, and different still from what they'll make for $1b. By truncating the reward distribution at $10mm, you tell those people to pursue something else instead.

Bezos is actually an excellent example. In his career at DE Shaw, he was almost certainly making very high 6 figures or maybe even 7, or certainly on a career track to be doing so shortly. He threw that away to take a massive personal risk to build Amazon. Would he have done that if you capped his potential reward at $10mm? Or would he have stayed in his comfortable finance job, making a bit less than that?


> He threw that away to take a massive personal risk to build Amazon. Would he have done that if you capped his potential reward at $10mm?

The unexamined premise of this question is that society at large benefits from the existence of Amazon and should want to encourage the creation of similar Amazon-like enterprises.


> The unexamined premise of this question is that society at large benefits from the existence of Amazon

It's not actually a premise, though. The point is that there are good ideas that take large personal risk and investment to build. Swap in Google if you prefer, or any other successful company.

That being said, Amazon is pretty clearly enormously beneficial. AWS alone has enabled thousands of companies that never would otherwise have been able to exist, and saved other companies millions of dollars on hardware, not to mention saving electricity (by better utilization), etc.

Every time a company gets big people whine and then vote with their dollars by shopping there anyway. Why do they do that? Because it benefits them. People buy things from Amazon because it's better. Amazon makes a profit that is smaller than that value delta - the residual is the consumer surplus, aka the net benefit to you and me.


> Swap in Google if you prefer, or any other successful company.

The unexamined assumption in this statement is that giant multinational megacorporations are good and we should encourage them.

I reject the assumption in your last paragraph that individuals making their own self-interested choices always maximizes positive outcomes for society at large: https://en.wikipedia.org/wiki/Tyranny_of_small_decisions


> The unexamined assumption in this statement is that giant multinational megacorporations are good and we should encourage them.

There is no unexamined assumption. Swap in whatever you want.

> I reject the assumption in your last paragraph that individuals making their own self-interested choices always maximizes positive outcomes for society at large: https://en.wikipedia.org/wiki/Tyranny_of_small_decisions

I don't disagree. But the default assumption always ought to be that it indeed does maximize utility, because it usually does, or approximately does. If you want to make the case that there's some better pareto-optimal equilibrium that Google and Amazon are disrupting, i'm more than happy to listen, but I think you're going to find that case a lot harder to make than you think.


Exactly. I would argue that the existence of giant, monopolistic companies like Amazon leads to increased income inequality and social instability. We shouldn't be figuring out how to order our economy to make more Amazons, we should be trying to reduce the harm of the current ones with stronger employee protections, stronger consumer protections and stronger anti-trust enforcement.


Considering that Bezos derives the vast majority of his wealth through capital gains as opposed to income, I'd say yes.


That's avoiding the issue. If the tax code were such that capital gains and all other income was captured, your parent's logic holds. The loopholes of the current tax system doesn't affect theoretical considerations.


Regardless, the theoretical considerations are a straw man. No serious progressive tax scheme results in a hard cap of income at something as low as $10m.


Ok, and how does the soft cap change the argument?


It means the ordering remains monotonic. It means if you’re on top of the world, you remain so with all the psychological trappings, just on a slightly lower mound. The scraps that come from slightly lowering your absolute position (but keeping relative position the same) will go to addressing externalities and common goods.


> It means the ordering remains monotonic

Are you willing to work as hard for $1 as for $1000, even if your relative status remains unchanged?

> The scraps that come from slightly lowering your absolute position (but keeping relative position the same) will go to addressing externalities and common goods.

Yes, but the entire point of this paper is that those 'scraps' are actually worth less than the economic gains produced by the ideas that receive these high top incomes.


I'm struggling to think of a progressive tax scheme that calls for 99.9% tax rate even on the highest bracket. $1 vs $1000 is such a bad straw man I'm not sure why you'd weaken your argument with it.

> the entire point of this paper is that those 'scraps' are actually worth less than the economic gains produced by the ideas that receive these high top incomes.

I'm not convinced by this. Every successful person who has created immense value for the world stood on the shoulders of not only giants but thousands of little people contributing to society. Those top income receiving ideas mean nothing in a society with no law, infrastructure, education, or opportunities. You think taxes stifle innovation? What would Bezos have accomplished had he been born to an uneducated militant in current day Syria?


> I'm struggling to think of a progressive tax scheme that calls for 99.9% tax rate even on the highest bracket. $1 vs $1000 is such a bad straw man I'm not sure why you'd weaken your argument with it.

Choose your own numbers. I made the argument because the point isn't the numbers, the point is that attenuating the reward distribution changes human capital decisions.

> I'm not convinced by this. Every successful person who has created immense value for the world stood on the shoulders of not only giants but thousands of little people contributing to society.

In what way does the necessity of infrastructure, both social and physical, contradict the point of the paper?


> the ordering remains monotonic

That only holds true if you assume people will act the same exact way and with the same exact outcomes. This is a silly assumption to make when you significantly change both the incentives and the difficulty.

> The scraps ... will go to addressing externalities and common goods.

What world do you live in?


Why do you equivocate progressive taxation with "truncating" income at a certain level? It's not a low-pass filter.


Just because it's easier to state. The same reasoning applies for a progressive tax rate system with extremely high top marginal rates.


after decades in Silicon Valley, I think that execution matters much more than the idea. Uber was not alone, Amazon was not the only bookstore, Google was not the only search engine.


You need to think of ideas about better execution (including the idea to focus on execution in the first place) as ideas.


What this fails to account for is that the tax raised by taxing the top incomes also has benefits for society - through government spending.

It's a trade-off: higher tax revenues vs higher innovation.

I suspect that the impact of higher taxes on innovation would be relatively small compared to the benefit of higher tax revenues.


Why would there be more benefit to me if money is spent by my congressman vs. by Bill Gates?

This is the difference between spending other people's money and your own.


So many great ideas are horrible businesses. Not sure exactly how that is going to be done in reality but interesting perspective.


> So many great ideas are horrible businesses.

Maybe, but great businesses are usually based on good ideas.


Sure that's not the point though. If you tax ideas and they are shitty businesses are you going to allow people to deduct that too?




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