Democratic presidential candidate Elizabeth Warren has had a long-standing call for a 2% wealth tax on any individuals with a net worth exceeding $50 million, and a 3% tax on wealth exceeding $1 billion. Yet when pressed on how to pay for her “Medicare for All” plan, Warren upped the ante to a 6% wealth tax for those fortunes exceeding $1 billion. (As I noted at the time of the announcement: If Warren doubles her wealth tax during the campaign, imagine how fast it will rise if she’s actually elected.)

Naturally, many conservative and libertarian analysts recoiled from such an economically destructive proposal. One of the ways critics used to illustrate the severity of Warren’s idea was to translate a wealth tax into an “equivalent” income tax on dividends, interest, and capital gains. But other economists pointed out problems with that line of attack, because after all, wealth and income are different things, and so taxes on them affect behavior differently. Wealth taxes are inefficient, no doubt about it, but not because “it’s the same thing as a huge income tax.” In the present piece I’ll try to referee the disputes and present the reader with an intuitive understanding of the issues involved.

How Wealth Taxes Can Correspond to Very High Income Taxes

In order to show that Warren’s seemingly modest 6% wealth tax was in fact quite radical, Richard Rubin at the Wall Street Journal warned that “Warren has unveiled sweeping tax proposals that would push federal tax rates on some billionaires and multimillionaires above 100%.” Likewise, Columbia University economist Wojciech Kopczuk—while commenting on the more academic proposal coming from economists Gabriel Zucman and Emmanual Saez—argued that, “If you consider a safe rate of return of, say, 3%, a 3% wealth tax is a 103% tax on the corresponding capital income and a 6% tax rate is a 206% tax.”

Before proceeding, let’s illustrate Kopczuk’s argument with a numerical example. (Note that in the rest of this article, in my examples I’m going to use small amounts of wealth, such as $1,000, to keep the math simple. Warren’s actual proposals of course only apply to wealth exceeding $50 million and $1 billion—at least so far!)

Now then, suppose someone starts with $1,000 in wealth. If he consumes it, then he faces no wealth tax nor income tax. (Kopczuk adopts the convention that any wealth taxes are assessed on wealth at the end of the period, while income taxes are based on income generated during the period.)

However, suppose the individual invests the wealth in fairly safe bonds that yield a return of 3%. At the end of the period, the individual will have the original $1,000 plus the $30 in gross interest income, for a new level of wealth of $1,030. If that wealth is then taxed at 3%, the individual owes the IRS ($1,030 x 3%) =  $31 (with rounding). Yikes! The income generated by that wealth was only $30 during the period, and so if the individual had the same liability from a income tax (applied to interest), then the “equivalent” tax rate would be 103%!

In General, a Wealth Tax Is Not Equivalent to an Income Tax

Although such calculations may be useful to wake up the average American to just how economically destructive even a “low” wealth tax may be, strictly speaking it is incorrect to argue that a wealth tax of x% is “equivalent to” or “the same thing as” a tax on capital income of y%. Over at EconLog, economists Scott Sumner and David R. Henderson both laid out some of the problems.

For our purposes, let me focus on Henderson’s commentary, where he showed the problem with Kopczuk’s analysis. Note, however, that in his actual example, Henderson ran the numbers for a 2% wealth tax. I’m going to change the calculations to make his same point, but using a 3% wealth tax, because I think that’s easier for the reader and also to be consistent with my commentary above:

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 [3%], leaving the owner with [97%] of $1,030, which is [$999.10].

Now raise the rate of return to 4%. With a wealth tax, $1,040 is taxed at [3%], leaving the owner with [97%] of $1,040, which is [$1,008.80].

How much more did the owner of capital net from the investment at 4% rather than at 3%? [$1,008.80] minus [$999.10], which is [$9.70]. In other words, for an extra income from capital of $10, the owner kept [$9.70]. The wealth tax amounted to a [3%] tax on the income from capital. [David R. Henderson, bold added, with bracketed numbers reflecting Murphy’s tweaking of the size of the wealth tax.]

As Henderson’s example shows, in general you can’t take a given wealth tax and then translate it into the “equivalent” income tax. In his example, if an investor has the choice between Investment A that is relatively safe and carries a return of 3%, and Investment B that is riskier but promises the higher expected return of 4%, then the wealth tax of 3% provides different incentives than a tax on capital income of 103%.

Specifically, under a 3% wealth tax, the investor who takes on the extra risk by switching to Investment B—trying to boost his gross rate of return from 3% to 4%, and hence his gross income on the investment from $30 to $40—will be able to keep 97% of that extra $10 in expected return on the investment.

In utter contrast, if the investor faces not a wealth tax, but instead a tax on capital income of 103%, then even if the riskier investment pays off as expected, the investor ends up worse off! Specifically, if he goes with Investment A our investor ends up with $1,030 gross on which he must pay ($30 x 103%) = $30.90 in income tax, leaving him with $999.10 after the dust settles. But if he goes with the riskier Investment B and even if it pays off as he’d hoped, the investor ends up with $1,040 gross on which he must pay ($40 x 103%) = $41.20 in income tax, leaving him with $998.80 when the dust settles.

In summary, David R. Henderson has come up with a specific example to show why it’s wrong to argue that a wealth tax of 3% is “equivalent to” a capital income tax of 103%. If we assume an investor has the option of putting his wealth into a riskier investment with a higher rate of return, then the 3% wealth tax only distorts the decision by 3% (loosely speaking). If the risker investment pays out, then the investor’s upside is only clipped by the modest 3% tax on the extra wealth he now holds. In contrast, under a 103% income tax, then it would be insane for the individual to even consider the riskier asset. Perversely, the more it pays out, the worse off the investor ends up, because the government assesses a tax that is proportional to, but bigger than, any gains.

At this point, we see that wealth and income taxes can have very different effects on investor behavior. Generally speaking, if we are considering long-term deployments of financial capital, and comparing it to a no-tax baseline, a modest wealth tax will lead investors to seek riskier assets earning higher (expected) rates of return, while a very high capital income tax will lead investors to tread water, putting their wealth into safe assets that earn very low rates of return. Both types of taxes distort financial decisions, but they do so in different ways. They aren’t “equivalent” in general.

Still Not the Full Story

My apologies dear reader, but we’re not done yet: Henderson’s analysis isn’t the full story, either. Strictly speaking, what he showed is that under a wealth tax of 3%, an investor who consumes all of his wealth at the end of the period only faces a marginal income tax rate of 3%. Yet in practice, most investors probably aren’t planning on consuming everything in one fell swoop, and so Henderson has led readers to understate the economic impact of a wealth tax.

Recall the example: An investor who switches his $1,000 in capital from an asset yielding 3% to one that yields 4% will see his gross income jump from $30 to $40. Henderson reasoned that under a wealth tax of 3%, the investor got to retain $9.70 of the extra $10 in gross income, and concluded that the marginal income tax rate was therefore only 3%.  (A reminder to avoid confusion: In order to keep the analysis comparable to the quotation from Kopczuk, I amended Henderson’s numbers to deal with a 3% wealth tax rather than a 2% version.)

Yet to repeat, this is only true if the investor consumes that $9.70. If instead the investor holds it another period, then it will trigger a second tax liability under the wealth tax, this time of ($9.70 x 3%) = 29 cents. And then if the investor carries the balance forward yet again, at the end of the third year he must pay another ($9.41 x 3%) = 28 cents in wealth tax. In contrast, under an income tax regime, if the investor just sits on his after-tax wealth after he earns it the first year, rather than deploying it to earn new income, then he owes no more additional tax on it.

In short, if our hypothetical investor had long-term plans for his wealth, then Henderson underestimated the burden of the wealth tax. In the limit, if the investor earned a one-shot return of $10 and then put it somewhere earning no return, it would asymptotically approach $0 over the years, as the government kept nibbling 3% annually at it. (For example, after 20 years of getting hit with the wealth tax, the original $10 in extra interest income earned that first year would have been whittled down to about $5.44.)

Let’s do one last example to illustrate the subtleties involved. Suppose our investor earned that extra $10 during this year (by moving his $1,000 into an asset that yielded 4% rather than 3%), and then wants to put the $10 under his mattress, where he intends to keep it for 50 years. How then would this extra $10 he earned this year, affect his long-term tax liability? Well, at the end of the first year he owes 30 cents. At the end of the second year he owes 29 cents on the remainder, and at the end of (say) the 25th year he owes 14 cents. However, when computing the burden from today’s perspective, those future tax payments need to be discounted. Since Kopczuk and Henderson both assumed a “safe” return of 3%, we can use that for a discount rate. (For example, the 14-cent wealth tax liability due in 25 years only has a present discounted value to our individual of 7 cents.)

Using this approach, the total wealth tax (in present-dollar terms) that the incremental $10 in wealth will cause our investor, over a 50-year time horizon, is some $4.89. In that sense, then, when our investor is considering whether to rearrange his portfolio in order to earn an extra $10, he faces a “marginal income tax rate” of about 49%.

Another way of showing the issue is to assume our investor wants to set aside a portion of his initial $10 in extra wealth, in order to cover all of the future wealth tax payments over the 50-year horizon. If he puts his earmarked “sinking tax fund” wealth into the relatively safe asset yielding 3%, then the investor must allocate $6.01 of his initial $10, just to cover the future wealth tax payments. Using this approach, the investor could understandably conclude that of his $10 in gross earnings—since he could only put $3.99 under the mattress “free and clear” for use in 50 years—he effectively paid the equivalent of a 60.1% marginal income tax rate.

Conclusion

Putting aside the moral problems with taxation—it’s theft, as a popular libertarian slogan reminds us—Elizabeth Warren’s proposed wealth taxes will have devastating consequences on capital formation, and will encourage investors to hold riskier assets than they otherwise would have. In order to illustrate the magnitudes involved, some analysts translated Warren’s proposals into “equivalent” income tax rates.

However, wealth and income are different concepts, and in general taxes on wealth and income will have different effects. For those investors with a short planning horizon, a modest wealth tax has a relatively modest impact on the decision to save for the future. However, for those with longer time horizons, even a seemingly modest wealth tax has an economic impact akin to a large income tax.