# Modelling a Wealth Tax Correctly

(This was written in response to Paul Graham's post Modelling a Wealth Tax).

## What is it?

A wealth tax works this way. A person pays a part of their wealth every year to the government. Take an example of a person worth \$110 million being assessed by Senator Elizabeth Warren's wealth tax, which would take 2% of all wealth above \$50 million. Such a person would pay 2% of (\$110m - \$50m). That's \$1.2m. Not that much, some might say. Senator Warren sells it as "just two cents!" on every dollar.

But the wealth tax is assessed every year, so this effect compounds. Our hypothetical millionaire is now worth a mere \$108.8m, assuming that she used all the return from her investments to live a comfortable lifestyle. Next year she'll pay 2% of \$58.8m - \$1.17m. And on and on. Supposing she lives 60 years more, spending all the growth of her investments, her \$110m would become \$68.2m. After 100 years, it would be \$57.9m. No matter how long she lives, her wealth won't drop below \$50 million due to this wealth tax. (Google sheet)

## Paul Graham's argument

I can understand why the super rich would want to fight the wealth tax, there's nothing surprising about it. What's interesting to see is how they do so.

Paul Graham is a venture capitalist with considerable success in his past. He is a partner at VC firm Ycombinator, which has funded several successful startups. It's top alumni include Airbnb, Dropbox and Stripe - a list that speaks for itself. He is wealthy enough that he would be affected by Senator Warren's proposed tax.

He recently published a post arguing against a wealth tax here - Modelling a Wealth Tax. He starts his explanation of the tax with:

If the wealth tax applies to all your assets, it's easy to calculate its effect. A wealth tax of 1% means you get to keep 99% of your stock each year. (emphases mine)

Strange. No one is proposing a tax that would apply to all your assets. This assumption actually muddies the waters, making people believe that they could lose a massive portion of their wealth, regardless of how wealthy they are. If you told the average Joe that they could potentially lose 2/3rds of their total wealth to taxation, they'd be terrified.

Later, he explains with an example - a "successful" startup founder.

Suppose your stock is initially worth \$2 million, and the company's trajectory is as follows: the value of your stock grows 3x for 2 years, then 2x for 2 years, then 50% for 2 years, after which you just get a typical public company growth rate, which we'll call 8%.

Within the space of 6 years, this founder has turned stock worth \$2 million into \$162 million, continuing to grow at 8% annually. Remarkable. PG implies this is a typical founder's trajectory. He doesn't mention the \$162 million number, preferring to say only that the founder started with \$2 million (like an average Joe).

A 2% wealth tax with a \$50 million threshold takes about two thirds of a successful founder's stock.

Did you notice the sleight of hand? PG talks about taking the founder's stock rather than wealth. He does that because it allows him to make that specific claim - that 2/3rds of the stock goes to the government. But let's measure wealth instead, because the value of that stock appreciates with time. He himself mentions growth of 8% - let's plot wealth according to his starting conditions and assumptions.

Whether or not there is a wealth tax, the founder still ends up with billions of dollars in wealth either way. Certainly she might pay hundreds of millions in wealth tax, but being a billionaire is still a fantastic outcome.

Let's make just one assumption - inflation for the next 60 years will be 3%. That allows us to calculate the value in today's dollars.

Wealth after 60 years Wealth after 60 years (in 2020 dollars)
With 2% wealth tax \$5.04B \$881M
Without 2% wealth tax \$15.18B \$2.65B

We can also account for living expenses. Assuming that the founder spends \$5 million every year on living expenses, they're still going to be a billionaire.

Wealth after 60 years Wealth after 60 years (in 2020 dollars)
With 2% wealth tax \$1.07B \$188M
Without 2% wealth tax \$6.38B \$1.11B

You can play with all of the data in this Google Sheet. Blue cells encode initial assumptions. Feel free to modify them and see how the chart changes.

PG's attempted sleight of hand avoids mentioning

1. How much the founder started with. He merely says "successful" when he means \$162M.
2. How many founders end up crossing the \$50M barrier, although that's most pertitent.
3. Why that 8% growth isn't accounted for. He inexplicably chooses "number of shares" instead of dollars as a metric for wealth.
4. How much that founder still has in their pocket after 60 years - hundreds of millions at the least.
5. Why that time horizon is so long. How many people make \$162M by the time they are 30 and then live to 90?

He would prefer you focus on the table which shows a lot of the stock (not wealth) evaporating. This is deliberately misleading. To me, this feels like scaremongering against a possible wealth tax. He wants to elicit sympathy from us for a person who starts with \$162M, spends lavishly (\$5M per year) and still ends up wealthier than they are today.

## Why a wealth tax might not work

That does not mean a wealth tax is simple to execute or that it has no downsides.

Proponents appear sure - it will greatly increase the government's revenues, while also reducing the wealth and influence of the richest people. Here are a few problems with implementing such a tax.

• They assume that the superrich can't just leave. This is not true, except for America which is highly effective at taxing it's citizens who live abroad. Proponents therefore assume the superrich will pay hundreds of millions of dollars in tax over the course of decades for the privilege of remaining American citizens.
• They assume that it's easy to institute such a tax. In most countries, it would require passing a bill in Parliament with a simple majority - easy. In America, it would likely require a Constitutional change, making it difficult. The only country that can effectively collect the tax would find it difficult to pass the law.
• A good accountant only costs a fraction of what some of these folks could lose every year. There's a myriad of ways the money could be structured or hidden to avoid most of the tax. The government's take might be small change and it might spend more trying to enforce this tax than what it gains.

And there are second order effects that we cannot predict. We could model it, but I think any model would merely reflect the biases of the model's author.

• The wealth tax might reduce the incentive for people to quit comfortable jobs and take a risk with a startup. It's possible startup founders and small business owners think that \$50m or less isn't worth the risk of starting up, that \$100m is absolute minimum, and that losing any of it to a wealth tax would make starting up a new business not worth it. Or maybe a wealth tax is the regulatory straw that breaks their back. If they think either of these things, we would see fewer startups and small businesses, leaving the economy with worse outcomes.
• Wealthy people who are angel investors might become wary of investing. Right now there's no possible way for them to lose their money. They will almost certainly be richer next year than they were this year, unless they do something reckless. They can afford to fund a few moonshots. However, if they're losing 2% of their wealth every year, they might choose to play it safe, leading to angel funding drying up. Again, fewer startups and small businesses.

I'm up front with my own ignorance about this. I don't know what the potential revenue will be, or what the future will hold, or how people will react to the new incentives. I just wish that folks on both sides of this debate would speak with a little more honesty.

## Will we ever see a wealth tax?

I don't think so.

It's popular with voters. In America, a majority of both Democrats and Republicans support such a tax. In the other corner we have rich people armed with money, influence and accountants, determined to prevent it from ever being successful.

It'll be a political issue for at least the next 15-20 years, especially as wealth increasingly concentrates in the hands of the few. We'll hear politicians promise it but it may never come to fruition.

I'm deliberately not writing about the implications of wealth accumulation and inequality on society. It's impossible to do it justice in a short post. In case you'd like to learn more would recommend reading the introduction to Capital in the 21st Century by Thomas Piketty. I found his explanation concise and coherent.

Thanks to Chandra Sekar, Minesh Patel and Rajat Khanduja for reading drafts of this and suggesting improvements.

Thanks to Arathi Sundarram for helping me with Google Sheets.