
Taxing Top Incomes in a World of Ideas [pdf] - barry-cotter
https://www8.gsb.columbia.edu/faculty-research/sites/faculty-research/files/finance/Macro%20Workshop/toptax.pdf
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barry-cotter
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.

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soVeryTired
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.

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nabla9
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.

~~~
soVeryTired
> 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?

~~~
nabla9
> 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.

~~~
soVeryTired
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?

~~~
nabla9
> 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.

~~~
soVeryTired
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...](http://irfanlal.yolasite.com/resources/N.%20Gregory%20Mankiw%20Macroeconomics%2C%207th%20Edition%20%20%20%202009.pdf)

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jacknews
"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.

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mirajshah
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.

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yorwba
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.

~~~
dahfizz
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).

~~~
alkonaut
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.

~~~
rollthehard6
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.

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

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johnNash05
I need these tax papers in docx format. Can I use PDF Converter for this?
[https://www.coolutils.com/TotalPDFConverter](https://www.coolutils.com/TotalPDFConverter)

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nobodylovesmeee
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...

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darawk
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.

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sooheon
> 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.

~~~
darawk
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.

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olivepistacchio
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.

~~~
1123581321
You need to think of ideas about better execution (including the idea to focus
on execution in the first place) as ideas.

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cjg
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.

~~~
hackeraccount
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.

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

~~~
lazyjones
> _So many great ideas are horrible businesses._

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

~~~
ThomPete
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?

