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Wealth and taxes, part I - Barokong

(This is Part I of a series. See theoverview for a summary. The punchline comes in Part V.)

Last November I had the pleasure of discussing "Top Wealth in the United States: New Estimates and Implications for Taxing the Rich" a very nice paper by Matthew Smith, Owen Zidar and Eric Zwick at the NBER asset pricing meetings, presented by Eric. The paper prompts a series of blog posts on wealth distribution and wealth taxes. I'll try to stick to points that haven't been made a hundred times already.

The paper mostly examines  Saez and Zucman's 2016 QJE paper on wealth inequality.  As many others have found, the Saez Zucman numbers are, ... let's say somewhat overstated.

Their bottom line is to cut Saez and Zucman in half. As I read the paper I think this is conservative -- and when we ask the obvious questions that the whole enterprise begs to be asked (which Smith et al don't do, but I will) a chasm of emptiness opens up, and the questions end up emptier than their answers.

The first thing you have to understand is the nature of wealth. Here is most people's impression of what wealth is:

That's not it at all. As Zwick et al say,

“Less than half of top wealth takes the form of liquid securities with clear market values”

So, the question is how do we measure the "wealth" that is not liquid securities with clear market values, like the profits of privately owned businesses? And, given that there is not US data on wealth (yet, thank goodness), even the part that is a security is hard to measure.

Enter "capitalization." The main idea in Saez and Zucman, reexamined by Smith et al., is that we measure "wealth" by measuring income, and then translating that income to wealth by assuming it will last forever and discounting it at some rate. In equations

Wealth = Income / discount rate

We have data from the IRS on income. So, let's follow along on Zwick et al.'s best story, how we find wealth invested in bonds from IRS individual interest income data and total bonds outstanding data:

“In 2014, the aggregate flow of [taxable] interest income was $98B, and the stock of fixed income wealth was $11T. The ratio gives the average yield, r = $98B/$11T   = 0.89%. Using this yield to capitalize income amounts to multiplying every dollar of interest income by 1/0.89% = 113 to estimate fixed income wealth. … Implementing equation (4) for fixed income gives an estimate of top fixed income wealth of $42B × 113 = $4.7T of fixed income wealth held by the top 0.1%. The bottom 99.9% estimate is $56B × 113 = $6.4T .
My emphasis.

You may have wondered, if we're just going to mulitply income by a number and call it wealth, why are we bothering to measure the wealth distribution at all? Let's just use the income distribution! You get one answer here -- if you call it wealth you get to multiply by 113! Since only some kinds of income get this treatment, kinds that are more likely to be held by wealthy people, that makes the numbers look much more unequal.

Smith et al's point though is not this basic one. Rather they look carefully at the calculation. This calculation assumes that all "fixed income" assets pay the same, low, rate of interest. Another well established fact is that rich people get better rates of return on their assets.

Here is Smith et al's plot of the actual rate of return that people earn on their fixed income investments. The uber wealthy earn 6% on their fixed income investments. This is not a small effect. In our capitalization factors, wealth = income / discount rate,

1/0.01 = 100

1/0.06 = 16.7

Changing from a 0.01 discount rate to a 0.06 discount rate pulls the wealth estimate per dollar of income down from 100 to 16.7. That's a lot. Smith et al:

“the adjustment reduces the top capitalization factor—and thus estimated top fixed income wealth—by a factor of 4.7, or 80%”
This is huge, to say the least.

(Note the irony. People who worry about wealth inequality are usually bemoan the fact that rich people earn higher returns on average than not so rich people, as it apparently will make inequality worse over time.  But the same higher average return must mean a lower multiples for converting income to wealth. You just can't have it both ways.

Higher returns are not some evil plot. The largely come from the fact that rich people buy riskier assets, like stocks and  junk bonds, and less rich people buy safer but lower yielding assets like bank accounts.  OK, It is to some extent a plot. Lots of regulations prohibit lower income people from buying the kinds of assets that make rich people richer in the name of consumer protection. The SEC is loosening some of these regulations.)

Beyond fixed income, the capitalization game gets even muddier, in both papers. What income flow are you going to capitalize?

“In the case of C-corporation equities, the income flow is dividends plus [realized] capital gains."
I think that's an accounting mistake, common in this literature. You cannot take the realized capital gains as an "income" flow for capitalization purposes. Suppose you buy a stock for $1, and it grows to $100. You sell $10 of the stock, but now you only have $90 left. You can't keep doing this forever, as the capitalization assumes.  That's fundamentally different than the company is worth $100, makes a $10 profit and gives you a $10 dividend. I'll be curious to hear from better accountants than I whether you can sensibly capitalize realized capital gains. Onwards...

For S-corporation equities, the income flow is S-corporation  income. For proprietor and partnership wealth, the income flow is the sum of proprietor income and partnership income  [ “capital” income?].  In the  case of real estate, property tax is capitalized to estimate housing assets ….”
Ok, that's income, what is the discount rate?

“Private business returns are harder to estimate than fixed income returns because private business wealth is harder to observe than fixed income wealth…We focus on multiple-based valuation models”
So we go from multiples to estimate a multiple... This all seems rather circular.

The bottom line? The game, as announced by Saez and Zucman is this: We start with the  pretax value of “capital” income, including asset income, proprietor income and partnership income, but not labor income (wages, bonuses, etc) or social security income. We multiply by various huge 1/r numbers to call them "wealth".  By doing that and using low r numbers, the "wealth" distribution looks much more extreme than the income distribution. As you can see the 1/r assumption allows great latitude in how this calculation is going to come out.


I spent a lot of time in asset pricing, and this paper was presented at an asset pricing meeting, so let me offer a little bit of what asset pricing has to say about these kinds of procedures.

The real capitalization formula is

P/D = 1/(r-g)

the price - dividend ratio is equal to one over the difference of the discount rate and the growth rate of dividends. Shhh! If the wealth inequality crowd realizes they can subtract g their multipliers will explode! (Joke. Of course we always use the right numbers)

The function 1/(r-g) is very sensitive to r and g, especially for low discount rates like the 1% we were using for bonds. Going down from 2% to 1% doubles the value. So, if you want to fiddle with values, fiddle with discount rates.

The right discount rate is much higher for risky assets than risk free assets. Lots of people discount things with stock market risk using interest rates, and get absurdly too high values.

If you put the 20 best financial economists in the world together in a room, gave them all of a company's cash flow information, they could not come within a factor of 3 of the actual stock market value.  "Valuation" mostly consists of fiddling with discount rates to get the "right" answer. Maybe "multiples" isn't so bad after all.

In short, capitalizing income to get any sense of "wealth" is an inherently... absurdly imprecise game.


I don't mean to sound critical of Smith et al. They're doing the best they can given the Zucman and Saez rules of the game. But a little peek into this sausage factory should leave you wondering, just why are these the rules of the game? Why do we care (should we care) so much about the distribution of something that is essentially impossible to measure or define? If you are making money was a partner in an LLC you help to run, why should anyone care about a fictitious accounting "value" of that partnership? You can't sell it!

Why start with pretax income? If you pay half your income in taxes, does that not halve the value of the asset?  Why does "wealth" include the value of proprietor and partnership income but not labor income or social security income?

These are good questions for the next few blog posts. Stay tuned.

On to Part II

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