03 Dec 2019

Wealth vs. Income Taxes

David R. Henderson, Economics, Tax policy 11 Comments

Ever since wealth taxes have entered the political discussion, I’ve been trying to put my finger on why they are even more destructive than income taxes.

Some early attempts had people arguing that–if we assume assets are earning 3%–then a 3% wealth tax operates just like a 103% income tax.

However, that wasn’t quite right, and it wasn’t showing how wealth vs. income tax have different impacts on investor behavior, regarding different types of assets.

David R. Henderson did a good job showing why this alleged equivalence is wrong. Specifically, he showed that someone who moved his wealth into an asset with a higher rate of return would only face an effective marginal income tax rate equal to the rate of the wealth tax. So for example, a 3% wealth tax “operated like” a 3% income tax, in this sense–not the really high 103% rate that previous commentators had suggested.

However, as I thought about David’s example, I concluded that it crucially rested on the implicit assumption that the individual would consume his wealth in the next period. So in my Mises.org piece, I showed what would happen if we extended the planning horizon to multiple periods. In that scenario, the wealth tax was a lot more punitive than the mere 3% rate that would occur after one year.

After you read that, though, strap on your safety belts and check out the following excerpt from my forthcoming Lara-Murphy Report article. I go back to a one-period analysis, but this time explicitly analyze the investor choice between a safe and risky asset. I couldn’t get to sleep the night I wrote my Mises.org piece, because I wanted to back up my intuition that a wealth tax pushes investors into riskier assets. I think I formalized the argument with this simple example. (And for sample issues of the LMR, see here.)


Nerds, Assemble: A Numerical Example Showing Why Wealth Tax Worse Than Income Tax

One of my pitches for getting people to subscribe to the Lara-Murphy Report is the promise that I will go more deeply into issues here, than in any other outlet. And so, let me show those of you who are interested, how I double-checked my intuition in the above section, to make sure there really is a legitimate sense in which a wealth tax is more inefficient than even an income tax.

In this example, we’re going to consider an investor who starts with $1,000 in financial capital, and is choosing between three possible options: (1) He can consume it now. (2) He can invest it in a very safe asset that will yield 5%. Or (3) he can invest it in a risky asset that half the time will appreciate 30%, but the other half with lose 10%. We are going to analyze the investor’s options, assuming three different tax environments: He either faces no tax, an income tax, or a wealth tax. We will calibrate the wealth tax to raise the same revenue as the income tax, in order to make it “comparable,” and then see which of the two taxes distorts the investor’s behavior more.

Things are pretty straightforward in the no-tax scenario. The investor can turn his $1,000 into a sure $1,050 with the safe asset, or he can go with the risky asset and have a ½ probability of ending up with $900 and another ½ probability of ending up with $1,300. In other words, he can earn a guaranteed 5% return, or he can earn an “expected” 10% return that carries with it more risk. (Without knowing more about the investor, we can’t say which of the two assets he will prefer, but we don’t need to know that for our purposes here, in analyzing the distortions of the two taxes.)

Now suppose the investor faces a 50% income tax, and goes with the safe asset. He is affected as I’ve show in Table 1, where “bop” stands for “beginning of period” and “eop” for “end of period.”

Table 1. Investor Faces 50% Income Tax, on an Asset Earning a Safe 5%

Wealth (bop) Gross Income Income Tax Wealth (eop)
$1,000 $50 $25 $1,025

Now let’s fine the “equivalent” wealth tax, for the investor going with the safe asset. That is, we want to calibrate the rate of the wealth tax, so that our hypothetical investor—if he goes with the safe asset—ends up paying the same revenue to the government:

Table 2. Investor Faces 2.38% Wealth Tax, on an Asset Earning a Safe 5%

Wealth (bop) Gross Income Wealth Tax Wealth (eop)
$1,000 $50 $25 $1,025

To make sure the reader understands Table 2: After earning the $50 in gross income from the safe asset, the investor has $1,050. But then he is hit with the wealth tax of ($1,050 x 2.38%) = $25. I deliberately chose the wealth tax rate of 2.38% in order to make the investor owe the same $25 that he had to pay under the income tax.

Let’s stop for a moment and assess our progress. We’ve seen that an income tax and a wealth tax both reduce the incentive to save. In reality the safe asset rewards the investor with 5% growth if he’s willing to postpone consumption for a year, but both taxes mute that benefit, making current consumption look artificially more attractive.

However, good economists know that we need to “think on the margin.” Even though I calibrated the wealth tax rate to yield the same flow of tax revenue to the government as occurred with the income tax, the two taxes still have different effects on behavior. An easy way for me to illustrate is to extend the analysis to see how the two taxes affect the investor if he puts his $1,000 of capital into the risky asset.

Table 3. Investor Faces 50% Income Tax, on Risky Asset That Gains 30% Half the Time But Loses 10% Half the Time

  Wealth (bop) Gross Income Income Tax Wealth (eop)
Good Outcome $1,000 $300 $150 $1,150
Bad Outcome $1,000 -$100 -$50 $950
Expectation   $100 $50 $1,050

(Note that in Table 3, we are assuming that half the time, when the individual faces the bad outcome and loses $100 of his original $1,000 investment, he gets a $50 credit on his taxes. In other words, his income tax liability is negative $50, as shown in Table 3. You can think of this either as him literally carrying forward the loss to future years, or you can think of the loss being used to reduce his gains elsewhere in his portfolio, thus lowering his tax liability in the current period.)

As Table 3 illustrates, when facing the income tax levied at a 50% rate, the individual who invests his $1,000 into the risky asset has a ½ probability of ending up with $1,150, and a ½ probability of ending up with $950. The expectation of these outcomes is $1,050, meaning the investor faces an expected (after-tax) return of 5%, in the risky scenario. Also notice that he expects to pay $50 in income tax—half the time he pays $150, and the other half he gets a credit of $50.

Finally let’s run the numbers for the wealth tax, when the investor goes into the risky asset:

Table 4. Investor Faces 2.38% Wealth Tax, on Risky Asset That Gains 30% Half the Time But Loses 10% Half the Time

  Wealth (bop) Gross Income Wealth Tax Wealth (eop)
Good Outcome $1,000 $300 $31 $1,269
Bad Outcome $1,000 -$100 $21 $879
Expectation   $100 $26 $1,074

Now we see how things get really complicated. In this last scenario, when the investor goes in the risky asset while facing the wealth tax (which had been calibrated to be “equivalent to” the income tax for the safe asset), he ends up with an expected return of 7.4%, and furthermore he only expects to pay $26 on average in the wealth tax.

Let’s summarize the big picture: Originally, in the no-tax scenario, the investor could choose between a sure 5% return, or a 50/50 return of either -10% or +30%, for an expected return of 10%.

When facing the 50% income tax, the investor could choose between a sure 2.5% return, or a 50/50 return of either -5% or +15%, for an expected return of 5%. So to reiterate, the income tax is inefficient, because it cuts the gains to saving in half; just compare the numbers in this paragraph with those from the previous paragraph. But the crucial point is that the income tax doesn’t distort the RELATIVE attractiveness of the safe or risky asset. In the no-tax scenario, the risky asset offered twice as high an expected return, but in exchange for an equally balanced up/down risk, and the same pattern holds when we introduce the income tax. So even though the income tax will make the investor less willing to save, it won’t distort what he does with those savings.

In contrast, when facing the wealth tax, the investor can choose between a sure 2.5% return, or a 50/50 return of either -12.1% or +26.9%, for an expected return of 7.4%. Again, compared to the no-tax scenario, our investor gets a lower return with either asset, and so he has less incentive to save. However, given that the investor is going to save and carry wealth forward in time, notice that the wealth tax has skewed things in favor of the risky asset. Rather than offering twice the expected return of the safe asset (2.5% vs. 5%), under the wealth tax it offers almost triple the return (2.5% vs. 7.4%).

And thus we see that the wealth tax introduces yet another distortion to economic behavior. It provides an artificial incentive for investors to shift their wealth into assets that are more volatile. To be clear, the problem here isn’t with investors going into risky assets per se. Rather, the economic inefficiency occurs because these risky assets look more relatively attractive than they actually are, in a no-tax landscape.

11 Responses to “Wealth vs. Income Taxes”

  1. Transformer says:

    The marginal tax rate on moving from a low return on capital to a higher one is lower with a wealth tax than an income tax (an extra $100 of income from capital will be taxed at 2.38% with a wealth tax but 50% for an income using your tax rates.

    But as far as I can see all that matters is average return – volatility doesn’t make any difference. If you just use a consistent 10% as the return in your example you get the same 7.4% return as you do with the more volatile example of averaging 30% and -10%.

    There is undoubtedly likely to be a correlation between return and volatility, but there may be other reasons for a higher return (investing in areas considered to be unethical for example), so I think this a valid quibble.

    • Bob Murphy says:

      Transformer what does this mean?

      “If you just use a consistent 10% as the return in your example you get the same 7.4% return as you do with the more volatile example of averaging 30% and -10%.”

      If you’re saying, “If you change the numbers you get a different result” then I believe you, but so what? Or am I misunderstanding your point?

      • Transformer says:

        You use an example where you get a return of 30% half the time and a return of -10% half the time, giving an average of 10%.

        My point is that you get (if I did not screw up my my quick calculation) exactly the same results if you just use a non-volatile return of 10% every year – hence my conclusion that it is the average rate of return and not the volatility that is driving the result.

        I would concede however that as generally (but not always) higher risk goes with higher volatility your conclusion that the wealth tax ‘ provides an artificial incentive for investors to shift their wealth into assets that are more volatile.’ remains true,

  2. Transformer says:

    I’m also curious to understand to what extent a wealth tax would be borne by the holders of wealth and how much passed on tin the form of higher prices for final goods.

    Assume that all wealth is held in the form of capital goods that are rented out. A wealth tax will reduce the return on all capital goods, making them less attractive to hold which will lead to a new higher tax-inclusive rate of return. If the demand for capital goods is relatively inelastic (as seems likely) then rents on capital goods will go up by an amount close to the value of the wealth tax. This will then be reflected in higher prices for consumer goods. The tax revenue will flow to the government and its beneficiaries who will spend the money as they see fit, while everyone else can buy less.

    I think to some extent this shifting of the burden of the wealth tax will also mask the effects Bob talks off . the long term effect will not be to make higher return, more volatile assets more attractive to hold. If the tax-inclusive rate of return for all capital goods increases to reflect the wealth tax the differentials in return between high and low risk assets will to a large extent be maintained.

    • Bob Murphy says:

      Interesting point, Transformer, I had thought in a perfect world I would build a model where investors bought real assets and then found the general equilibrium outcome of the different taxes, allowing asset prices to adjust.

      • Transformer says:

        I think that would be much longer post !

        Don’t get me wrong – I think your example highlights the likely distorianmary effects of a wealth tax using the simplest case – its just been my observation that most of the recent discussion on the wealth tax has tended to implicitly assume that the burden will fall exclusively on the holders of wealth.

        Actually, I think that even if owners of capital goods were able to pass on the tax in the form of higher rents then there would still be a move to riskier assets – but driven by the fact that rents on these riskier assets would increase by less than rents on safer assets rather than by wealth owners moving to obtain higher returns.

  3. baconbacon says:

    Scott and David are both wrong. Scott is wrong because he switches from averages to a single outlier year which distorts the conversation. Here is a direct quote from SS

    Consider the following analogy. An Illinois farmer has a 640-acre soybean farm, which usually provides an income
    of $140,000/year. In 2019 his income falls to only $10,000 due to low soybean prices. Suppose his annual
    property tax bill is $12,000. Would you say the farmer pays a 120% income tax rate? Of course not. And note
    that a property tax is similar to a wealth tax, but only applies to one type of wealth.

    In this example the farmer earns $140,000 a year over a long period of time, and then has a one time drop in earnings down to $10,000 a year. Lets say its 9 years at $140,000 and 1 year at $10,000, so he earns 1,270,000 over 10 years and pays 120,000 in taxes for a tax rate of 9.45%. Does it makes sense to say that the farmer payed the equivalent of a 9.45% income tax rate in this situation? Yes, in terms of economic behavior you would expect the farmer to roughly respond to a $12,000 property tax and a 9.45% income tax with similar behaviors, and yes it does make sense to say he paid a 120% income tax in one year, but it doesn’t make sense to include other years information in the set up and then not include it in the overall tax rate.

    David Henderson has done something equally incorrect. The complaint about the wealth tax acting as a 100% income tax is based on going from a 0% wealth tax to a 2% wealth tax. Henderson is starting from the point where the 2% wealth tax is already instituted and the calculating the marginal tax implications of earning more or less money after the fact. Watch what happens when you change the tax rate, not the earnings rate.

    $1000 earning 3% a year with a 2% wealth tax. $1030 at year end, taxed at 2% leaving $1009.40, increase the wealth tax to 3% and it leaves $999.1 after the tax. What is the marginal effect of increasing the tax rate from 2% to 3%? It is clearly not 1% of income.

    • baconbacon says:

      The proper way to think about it is as a substitution, lets say a country had a 25% tax rate on this type of income, and wanted to change to a wealth tax, what is the appropriate wealth tax to switch to at a 3% risk free rate of return. That is the question being asked, not ‘what is the marginal implication of a wealth tax on a person who made a 3% return on their money vs a 4% return on their money’.

  4. Ken P says:

    This is a great analysis. I thought wealth tax might impact risk appetite but wasn’t sure.

    My simplistic view is that if you tax capital you get less of it, resulting in lower marginal productivity and therefore lower wages. I would expect a 3% tax on Jeff Bezos in the past to have resulted in 3% less capital. If this were 3% less warehouse space, data centers, etc. each year then that is pretty impactful. Most of the internet runs on Amazon cloud servers and we would be much worse off if it didnt.

    • scineram says:

      But Bezos does not own a single warehouse space, data centers, etc. Amazon does, which is not subject to the wealth tax.

  5. Tel says:

    A tax is not “worse” if it raises more revenue, because the rate can always be adjusted.

    All government spending is always tax … either direct tax, or indirect tariffs, or inflation (tax by stealth) or debt (taxing the unborn). The moment that dollar gets spent by government, tax is owed.

    Therefore revenue is controlled by how much government spends … not by the method used to collect it.

    So, based on a fixed amount of money that is going to be collected one way or another, I put forward that income tax discourages labour and encourages people to either retire early, go into semi-retirement, or give up entirely and drop out because they don’t expect to ever achieve much. It’s a highly destructive tax.

    Wealth tax is also destructive (all tax is bad) but IMHO slightly less worse than income tax for an equivalent amount collected. Also tariffs are not too bad providing they are set at around the 10% mark. Wealth tax does not encourage people making an effort but it discourages the accumulation of non-productive capital. If you own an asset that returns 1% but the tax is 2% then you are better off selling that asset to someone else … which is a good thing because maybe the buyer can do something more useful with that asset.

    Now there’s the question of difficulty of collection. Well, income tax has a terrible load of completely deadweight government intrusion into every aspect of your life. It also contains some totally arbitrary calculations in terms of what happens to be considered a legitimate deduction (and that changes from time to time at random). So trying to be worse than income tax is a significant bar to jump. Wealth tax could probably be skipped on all small things (if I have a bunch of nice pens in my drawer, they might have some resale value but really taxing those kind of things is plain stupid) so the target will be large things: land (obviously) and houses, cash in the bank, cars, equities, and if you hold reasonable quantities of precious metals. Most of this stuff can be fairly accurately valued, the old trick of having a rule that if a valuation appears a bit low then government can buy that asset at the given amount could work.

    Also, government can tax the insurance company and then they build that into the insurance premiums. You insure your car for $20,000 and then that automatically becomes the official valuation of the car, and you automatically have paid asset tax on that car. Since most valuable things get insured, that’s likely to be the most common tax payment mechanism. If you have something valuable and you keep it secret without insurance then should it get stolen the first thing the police will ask for is an up to date tax certificate … if you don’t have that they figure they don’t need to bother doing any police work to recover that item.

    Government is really a protection racket, and the wealth tax more accurately reflects this. Income tax means they effectively own your labour while wealth tax means they are demanding a fee to protect your assets. There’s a difference.

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