The late great Armen Alchian taught me that you can be rigorous with words. As a math major, I needed to hear that. Last week, I forgot that. I let algebra distort my thinking.
In a post last week, I expanded on Columbia University economist Wojciech Kopczuk’s statement that a 3% tax on wealth amounts to a 103% tax on capital income from wealth. (This is in a case where the capital earns the riskless return of 3%.) I used algebra to fill in the missing steps.
Reader Daniel was not convinced, writing:
Dr. Kopczuk has a great paper full of compelling reasons on why we might prefer more “vanilla” taxation schemes than a wealth tax, but the “an X% wealth tax is actually a Y% capital income tax” line isn’t one of them.
Daniel also referenced my co-blogger Scott Sumner’s exposition of a similar point. I had read Scott’s piece quickly and had seen that he was referring to a news story in the Wall Street Journal in which reporter Richard Rubin had made a strong claim. It didn’t surprise me that an economist could find a flaw in a journalist’s economic reasoning about a complex subject.
Little did I know that Kopczuk made a similar mistake.
And I’ve now figured out how to show it.
The way to see what the marginal tax rate on capital income is is to think on the margin: change the income from capital and see how much extra tax is paid.
So, for example, start with $1,000 at the start of the year that earns what Kopczuk calls the riskless rate of return, 3%. With a wealth tax, $1,030 at year’s end is taxed at 2%, leaving the owner with 98% of $1,030, which is $1,009.40.
Now raise the rate of return to 4%. With a wealth tax, $1,040 is taxed at 2%, leaving the owner with 98% of $1,040, which is $1,019.20.
How much more did the owner of capital net from the investment at 4% rather than at 3%? $1,019.20 minus $1,009.40, which is $9.80. In other words, for an extra income from capital of $10, the owner kept $9.80. The wealth tax amounted to a 2% tax on the income from capital.
Of course, there are other taxes on capital. But I’m focusing here on the marginal tax rate on capital income due only to the wealth tax of 2%. It’s 2%, not the outlandish number I had thought.
Yes, you can attribute the whole tax on wealth to the tax on income. But there’s zero economic justification for doing so.
Bottom line: Think on the margin. With emphasis on “Think” and “margin.” Daniel was right, as was Scott.
READER COMMENTS
Rob Rawlings
Nov 25 2019 at 9:16pm
It seems intuitive to me that that increases in wealth due to returns on capital will (if none of the income is spent on consumption) lead to a marginal tax rate (ignoring any other taxes) on these increases equal to the prevailing wealth tax.
Example: If you get 3% return on $1000 you earn $30 and if the wealth tax is 2% (and you don’t consume any of it) your wealth increases by $30 so you pay $.6 additional wealth tax, which is equal to that 2% wealth tax.
As someone terrible at math I would be curious to know exactly what was wrong with the algebra in the original post.
BTW: Kudos to David for acknowledging his error.
Rob Rawlings
Nov 26 2019 at 9:39am
OK, I see now that if you calculate: tax_on_new_wealth / (tax_on_newwealth + tax_on_exisitng_wealth) then you come up with the 100+% tax rate. And David is now pointing out that this calculation makes no economic sense. So there was nothing wrong with his algebra, he was just calculating a meaningless value.
Rob Rawlings
Nov 26 2019 at 9:52am
I meant: (tax_on_new_wealth + tax_on_exisiting_wealth) / new wealth
Chris Stucchio
Nov 25 2019 at 9:33pm
I think there’s a bit of a mistake in your calculations, namely the fact that you’re treating “wealth” as static. In fact, wealth is strictly a function of future income:
Wealth = NPV(future income)
So what you’re actually saying to begin with is that NPV($30 yearly) = $1000.
However, the NPV($40 yearly) is $1,333. The result of this change in income is an increase in wealth taxes of $6.66.
So the marginal tax rate on additional income is 66%, unless you can somehow persuade the IRS to ignore the updated valuation of your asset.
As far as I’m aware, the wealth tax folks want to hire lots more IRS workers in order to compute yearly fair market valuations. So this seems unlikely.
Brandon Berg
Nov 25 2019 at 11:37pm
Keep in mind that unlike a tax on wage income, which is only levied once, a wealth tax will be levied over and over again. If you earn $100 in capital income this year and never spend it, you’ll pay $2 on it this year, $1.96 the next year, and so forth. The long-term marginal rate is much higher, asymptotically approaching 100% as your investment horizon approaches eternity.
Mark Z
Nov 26 2019 at 2:09am
I’m somewhat confused as to why how much of an increase in the rate of return one gets to keep is what matters ‘on the margin.’ If we think in terms of new saving/investment on the margin, doesn’t the old reasoning hold? E.g., if I have $100 I can either spend now or invest for a year and then spend it, if the tax rate is higher than the rate of return, my post-tax return is negative, the tax rate on my next investment is >100%. I suppose the $100 itself was income, and the capital gains from investing it is only a small part of the value I’m left with at the end, so perhaps I should actually be dividing by that instead. But even then, since the wealth tax is annual, the actual tax on my next $100 of income should I invest it isn’t just the wealth tax I pay on it this year but next year and the year after and so on. So, really, if the tax is levied for 10 years, we need to account for how much the tax will leave me after 10 years relative to how much I would’ve had absent the tax (I’m ignoring the inter-temporal discount rate of course). And this is still ‘at the margin’ if people are forward looking and try to account today for the increase in expected future taxes on income earned today.
Markus
Nov 26 2019 at 2:43am
I agree with Mark that the old reasoning was the correct one: usually we care about the distortions in the consumption-saving decision when taxes on capital are discussed. For that marginal decision of saving an additional amount, the old reasoning is correct.
A wealth tax is less distortionary, however, when the choice between different investment opportunities is concerned. I.e. with a capital income tax people potentially prefer safer assets with a lower return.
Michael Sandifer
Nov 26 2019 at 4:06am
We all make such mistakes at times. You’re a good economist. I wouldn’t worry about it.
Josh
Nov 26 2019 at 4:08am
I think your original analysis is still meaningful though. Take Sumner’s soybean farm example. If a farmer makes $100k in income every year but pays $120k in property tax (say 3% on his $4m farm), the property taxes are the difference between keeping the farm and being forced to sell it. The amount paid in wealth tax compared to the income earned on that wealth does matter, not just at the margin. It’s going to change behavior and not necessarily for the better.
In particular, for a tax on all wealth, it’s going to make spending money or holding riskier assets relatively more valuable. Eg with a 2% wealth tax, a risk free asset earning 3% now earns 1%. A riskier asset with a variable but expected return of 6% now earns around 4%. Before, the extra risk would double your expected return. Now the same extra risk more than quadruples your return. That matters. (And if the tax makes me switch from the 3% risk free asset to the now 4% risky asset, is that really what Warren or Saez want from this tax?). A similar story holds when comparing the value of an additional boat to the now smaller returns. (Does Warren really want to encourage the wealthy to own more boats?)
Honestly I think the changes in behavior are going to make the rich more off putting to people, not less.
robc
Nov 26 2019 at 7:47am
I don’t think buying the boat works, as that is still an asset and would count towards the wealth tax, right?
I think Warren is trying to re-enact Brewster’s Millions on a wide scale (without the payoff at the end).
robc
Nov 26 2019 at 2:51pm
One of the following 3 must be true in the soybean farm example:
If he is only getting $100k per year, he is a bad soybean farmer.
The land is appraised too high at $4MM.
The land is appraised correctly, but soybeans is not the highest use of the land, it should be sold off as an office park or something.
3% is about right for economic rents (I see estimates between 3 and 4), so a Single Land Tax would be at about that rate. Something is wrong in that being a soybean farm. I guess there is a 4th possibility: the tax rate is much higher than the rent rate (that is sort of a subset of #2, but technically different).
RPLong
Nov 26 2019 at 10:06am
Something about this analysis doesn’t sit right with me, and I’m not sure what it is.
If $1000 is earning a positive rate of return annually, then a 2% “wealth tax” is equivalent to a 2% reduction in the rate of return. If the $1000 isn’t earning a positive rate of return, then a 2% wealth tax is equivalent to a 2% increase in the rate of loss for the year.
This loss gets worse when we factor inflation into account. If the government levies a 2% wealth tax while the central bank maintains a 2% inflation target, then this seems deeply unfair. It also seems like a viable economic justification for attributing a 2% tax on wealth to income. 3% isn’t the risk-free return anymore if 2% is lost to wealth taxes.
There are implications here that are captured by Wopczuk’s argument that don’t seem to be captured in the above post. I am either deeply confused or something important is missing.
As an aside, according to this website, the median property tax rate in all 50 states was less than 2%. I don’t know much about Warren’s plan, but unless she intends to levy a nationwide federal property tax, we can expect a lot of this taxable wealth to “magically” turn into real estate holdings.
Rob Rawlings
Nov 26 2019 at 11:18am
I think what is being discussed in this post is the rate at which retained income generated by wealth is taxed. As shown this new wealth is taxed at the same rate as existing wealth.
However if the return on capital is (for example) 4% and the wealth tax is 2% then it does not seem unreasonable to say that the income on capital is taxed at 50%. In this case what is being calculated is the tax on the wealth as a % of income from the wealth. This rate will be correct even if none of the income is kept as new wealth. If the wealth tax is greater than the return on wealth then the tax rate will be > 100%.
AMT
Nov 26 2019 at 12:24pm
“Yes you can attribute the whole tax on wealth to the tax on income. But there’s zero economic justification for doing so.”
well I think it is a useful comparison to show how the wealth tax compares to an income tax. If you tax capital at 6% and it gets returns of 6%, that’s equivalent to a 100% income tax. Because it would be difficult to find political support for completely confiscatory rates of income taxes, it helps get around that through a “wealth” tax. Consumption and income taxes are less related, but given the fact that capital does generate income, I think it’s also relevant to consider how a wealth tax impacts incentives. If I recall correctly, I’ve also seen sumner say something along the lines of “all taxes are consumption taxes” so his point seems rather hypocritical there.
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