Thread by @joshgans

1/ Here is a tweetstorm explaining why @paulg is wrong and @vkhosla is right on why a higher income/wealth tax is unlikely to deter growth entrepreneurship.

@paulg @vkhosla 2/

Here is a simple example: suppose that a venture has a 1% chance of creating a $1 billion for an entrepreneur and 99% chance of creating nothing. Suppose that entrepreneur's other option is a safe Wall Street job netting $3 million over the relevant time period.

@paulg @vkhosla 3/

Without any tax, the expected return from being an entrepreneur is $10 million which is higher than the certain option of going to Wall Street. So the entrepreneur becomes an entrepreneur.

Now suppose that 50% (!) of income is taxed.

@paulg @vkhosla 4/ In this case, the Wall Street job nets $1.5 million while the expected return to being an entrepreneur falls to $5 million. So the same choice is made. If 70% of income is taxed, WS becomes $900K and entrepreneurship becomes $3m. Still no change.

@paulg @vkhosla 5/

The reason this all works is maths. If p = prob of start-up success, w = Wall Street income, u = start-up success income, t = the tax rate then you become an entrepreneur if tpu > tw or pu > w and otherwise don't. But the tax rate doesn't matter.

@paulg @vkhosla 6/

To be sure, t is an average tax rate. However, for both of these options, the average and marginal tax rates aren't that far apart. So why, you may ask, is Chad Jones (web.stanford.edu/~chadj/toptax.…) finding that a 30% is option to encourage innovation?

@paulg @vkhosla 7/

The reason is that he is looking at social welfare and not individual returns. But driving it is an idea that a higher marginal tax rate will reduce entrepreneurial effort.

Imagine you have already started your venture.

@paulg @vkhosla 8/ It is late at night on the weekend and you don't know if you can do any more. You think about the successful entrepreneur mentor. You realise that you could push a little more and increase your probability of success to p'.

@paulg @vkhosla 9/ If you do so, your return goes up by t(p' - p)u but getting some sleep gets you a benefit of b. At that point, if you compare 0.3(p' - p)u to 0.7(p' - p)u, maybe the tax rate matters.

Now imagine you are a venture capitalist, choosing to fund an entrepreneur.

@paulg @vkhosla 10/ Do you fund the entrepreneur for whom b is so high that the tax rate matters in the middle of the night? Or do you fund the entrepreneur who cares more about u than b per se?

@paulg @vkhosla 11/ Because for this to matter, if p' = 0.2 and p = 0.1, then we are imaging a situation where b is greater than $3 million but less than $7 million.

No, you want entrepreneurs where b doesn't matter and they push through regardless.

@paulg @vkhosla 12/ So I would argue that the Jones' postulated shift away from innovation as a result of taxation is way too high; especially given the low probability of success that amplifies these calculations.

The real barrier to the entrepreneur is the low probability of success.

@paulg @vkhosla 13/ In the end, that weighs more heavily than any changes in the top income tax rate.