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PaperclipPerfector  1yr ago (text post)   26108 thread views

Culture War Roundup for the week of December 4, 2023

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Let e be your risk aversion and let p be the the proportion of your portfolio you are investing in stocks

Where is “p”? I’m gonna need a template for these equations, like an article who uses similar ones (the wikipedia markowitz model wasn’t helpful). Or more letter definitions.

As taxes go up, k shrinks from 1 towards 0, which makes x increase. Therefore, capital gains taxes cause increased risk tolerance.

So a 99 % capital gains tax results in everyone investing in stocks?

The chief academic argument against capital gains taxes is that they impose a 100% tax on consumption in the far future, which is maximally distortionary.

I call bullshit on that. A 100% tax on everything right now is more distortionary.

I personally think that if society had no welfare, a flat income tax would be either not distortionary or push people to work more.

But we have welfare, and the income tax isn’t flat. You’re very theoretical today.

Note: historically people worked much more and (e.g.) wages being 4x lower because your country is poor is equivalent to a 75% flat tax today.

Ignoring the motivating effect of hunger, of course.

A wealth tax reduces returns by k:

x = ((A-k) - (i-k)) / (2ekkB) = (A - i) / (2ekB)

I think there’s an error here. The k subtracts itself in the numerator, so the two k’s stay in the denominator, unlike in the cap gains equation.

in case it wasn't clear, I'm saying a wealth tax is better than a capital gains tax in that it doesn't distort risk-taking while a capital gains tax does

Vast layers of misunderstandings keep peeling off, yet your position remains as inscrutable as ever. Didn't you (wrongly, see above) determine that the equation was the same : ' x = (A - i) / (2ekB)' for both? So why is risk tolerance increased for cap gains tax and not for the wealth tax?

I want to distort risk-taking, I think we would all tremendously benefit from a 90% reduction in financial risk aversion of the average citizen. By the lights of MPT, shouldn’t we collectively expect a higher return on all our investments if risk aversion went down?

Yeah. Note: people would probably save less, but what the people are saving would be invested in stocks rather than bonds in this model.

I think that discredits the model. They’re not going to take all the equity risk for 1% of the equity premium, they’re supposed to be loss averse.

Sure. I mean that according to ivory-tower theory, even a 1% capital gains tax now is equivalent to a 100% tax on far-future consumption.

This is a useless extrapolation theory.

I think a poll tax (and its opposite: welfare) is distortionary.

Welfare is not the opposite of a poll tax, it’s a progressive tax that goes into the negative. Regardless, how is a poll tax distortionary?

That's not what risk is. If the company he invests in goes bankrupt, that's not helped by the 99% capital gains tax. That is the risk he cares about, not the variance on his profits. But let's not get into that.

And it keeps going, more layers of misunderstandings.

x = ((A-k) - (i-k)) / (2eB) = (A - i) / (2eB)

So, my conclusion remains: the wealth tax doesn't affect the allocation into stocks, while the >capital gains tax does. This also explains your second point: the two conclusions are no longer the same.

So your math was incorrect, but luckily you interpreted it wrong, so by being doubly wrong you went all the way to being right again?

And what happened to the k’s now, why did you remove them from the denominator? You previously used them to justify “As taxes go up, k shrinks from 1 towards 0, which makes x increase. Therefore, capital gains taxes cause increased risk tolerance. “

By that logic, and assuming the equations are worth a damn, the wealth tax also causes increased risk tolerance. More even, since you have two k’s in the denominator going to zero.

Do you believe venture capitalists and the startups they fund are net-bad for society? I think they're (a) net-positive and (b) the platonic ideal of high-risk-taking, so I don't think we want to discourage risk-taking in general.

Another misunderstanding. Man, I am in favour of risk, from the beginning. Between low-risk/low-return and high-risk/high-return, I choose high every time. Personally, and macroeconomically. I said people should be less risk averse, ie, take more risk. I could rail against insurance companies and the giant societal loss they represent all day. They prey on the irrational fears of people to the tune of trillions of dollars annually. But that’s besides the point.

To be 100% clear, no, I do not believe VC and startups are net-bad for society at all.

what matters isn't that risk is reduced - what matters is how it was reduced.

I am not talking about a reduction in risk, but a reduction in risk aversion. An investor with less risk aversion (ie, willing to take more risk) could expect higher returns, correct? I’m just applying this to all investors in the economy.

Just to make sure we're on the same page - you're saying welfare is a "progressive tax that goes into the negative". A poll tax is a fixed sum demanded regardless of income.

Yes, and yes.

Your progressive tax depends on your income. When your income is low enough, instead of paying the tax, you get welfare. So it’s the ‘negative side’ of the progressive tax. Your progressive tax becomes a payment to you.

The poll tax is not distortionary, because nothing you do matters. You can work or not work, you’re still on the hook for the same poll tax, 100 dollars or whatever. The progressive tax( including welfare), takes from you if you work and gives to you if you don’t. Whether that is good or bad is another issue, but it definitely distorts your behaviour more.

So, in this model, a poll tax would cause me to work more.

Any tax in this model is distortionary. We’re talking relative distortionaryness.

If you want a story: consider someone who barely makes enough to survive - a poll tax would force them to work more hours to continue surviving.

That’s what I referred to above : “ignoring the motivating effects of hunger”.

I've been arguing this whole time that

  1. A wealth tax doesn't affect risk tolerance
  2. A capital gains tax reduces risk tolerance

Have you??? Then why does your model predict that a 99% cap gains tax cause people to put everything in stocks instead of bonds? You literally said 'capital gains taxes cause increased risk tolerance.'

Ah whatever, we’re all dullards. It’s just that I felt you were trying to Euler me, and your errors are not encouraging me to change my priors in future discussions that involve equations I don’t quite grasp. However, you’ve been nothing but graceful and civil, so let me try one equation.

U = ln(wage * labor - poll_tax) - labor

Why is the poll tax wedged in that parenthesis? It has nothing to do with labor or wage, it should be outside.

I believe the following is a more traditional view of poll taxes in mathematical form:

Let U be the daily utility function of a worker

Let W be the hourly wage in utils for work performed.

Let L be the labour in hours

Let I be the utility gained from idleness, hourly

(16-L being the hours in the day where he’s not working, not sleeping.)

U = W * L + I * (16 – L)

dU/dL = W – I

So the higher his wage, and the less he enjoys idleness, the more he will work.

Add in a poll tax to his utility function , and you get:

U = W * L + I * (16 – L) – poll_tax

the poll tax disappears in the derivative, and dU/dL = W – I again. Poll tax irrelevant.

Now for the income tax:

U = W * L * (1- income_tax) + I * (16 – L)

dU/dL = W - W * income_tax – I .

The income tax is still there. Increase in income tax results in less labour. Therefore distortionary.

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