Arnold Kling  

A Bet I Will Make

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Some comments on my post on Social Security challenged me to bet. Here is a bet I am willing to make. It concerns the following proof.

1. national output = national income (note that is true by definition in a closed economy, but in an open economy you can in theory earn income on other countries' output. Let's ignore the open-economy case here and assume a closed economy.)

2. national income = labor income + capital income + rental income + other

3. capital income = income accruing to shareholders of public companies + interest income + income of privately-held companies + other

4. Leaving out pathological examples that make certain types of income negative, it is impossible for something on right-hand side of one these equations to become larger than the left-hand side. For example, it is impossible for income accruing to shareholders to exceed all of capital income.

5. Therefore, income accruing to shareholders of public companies can never exceed national output.

6. If income accruing to shareholders grows faster than output indefinitely, then eventually income accruing to shareholders must exceed national output.

7. Therefore, income accruing to shareholders cannot grow faster than output indefinitely.

I will bet that you can find nothing wrong with that proof.

Many relevant time horizons are shorter than "indefinitely." Shorter time horizons may present investors with the opportunity to earn income that grows more quickly than the economy over the relevant time horizon. You are always welcome to make a bet on that by buying mutual fund shares. I have some myself, although these days my portfolio is lighter on U.S. stocks than usual. For Social Security., though, the time horizon you want to think about is pretty long.


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COMMENTS (16 to date)
Joel writes:

Still seems to me that two concepts are being confused here. What counts is the return to investment in equity capital, not the rate at which stock prices grows. If GDP is static, and profits are static, and stock prices are static, it doesn't follow that the return to equity is zero. Companies can still be profitable and paying dividends, and the dividend rate would be the return to the equity investor. Similarly, it doesn't follow that the return to equity investors in a growing economy (when they benefit both from the dividend rate and stock price growth) is limited to the rate of GDP growth.

RC writes:

Here's a bet I'm willing to make:

I'll be you that x + y = 5
-- You can pick any number for x (as long as it's 3)
-- Y can represent any number (let's ignore the fact that it can be any number other than 2)

It's pretty easy to generate a 'proof' that is self-fulfilling and indisputeable when you fill it with provisos and exclusions.

[Hand raised and gesticulating wildly] Oh, oh...call on me Professor.

Things wrong with your proof:
- The posts in response to your Social Security thread were thoughts as to how things functioned in 'the real world'. Your proof is not (by definition).
- Economies ARE open
- 'Other' leaves room for quite a fudge factor

I do, however, completely agree with you that anyone that thinks putting everyone's retirement into the stock market could in any way result in stable, guaranteed long-term benefits promised by the government to people is merely engaging in a thought excercise on replacing one Ponzi scheme with another.

Alex J. writes:
If income accruing to shareholders grows faster than output indefinitely, then eventually income accruing to shareholders must exceed national output.

Income accruing to shareholders could grow asymptotically. e.g. one year it grows 10%, the next 1%, the next 0.1% etc.

Steve Roth writes:

You forgot that credit/debt issuance -- by government but especially by financial institutions -- creates money. Manufactures it out of thin air.

And that credit/debt is decidedly *not* all issued in return for claims against real assets or their future products.

This can go on for a very long time. Has.

cf Dirk Bezemer:

http://mpra.ub.uni-muenchen.de/15766/

Especially this graphic:

http://www.asymptosis.com/wp-content/uploads/2011/01/Screen-shot-2011-01-30-at-4.53.13-PM.png

John writes:

Arnold, I'll willingly concede your argument is completely valid and irrefutable. I will also point out that valid argument is fully consistent with a false conclusion if one or more of the premises are wrong.

Jim Glass writes:

First, stocks can provide a return greater than the growth rate of the economy, and do so forever, for a simple reason: stock returns are simple interest, not compound.

This in fact is the way that stocks have always provided their high returns. Historically while the S&P has provided its 6% real, the capital value of the S&P stocks has grown only slightly faster than GDP. People consume a lot of their dividends. There's no reason why this couldn't continue forever.

Second, note that the SS Trustees say today's and future participants will take a net *loss* on their contributions of $17 trillion.

This is because SS is a paygo program, so total "tax collected" must equal "benefits paid" in the end. And early retirees, up through roughly today, have earned $17 trillion in benefits in excess of the taxes they've paid in -- is it any mystery why SS was so popular!?

But this also means future retirees -- starting with today's workers, age 40s or so and under -- must get back $17 trillion less than they pay in to reach "paygo balance". That is, they must pay taxes to cover their own benefits *and* pay $17 trillion more to prior workers for their benefits -- meaning, by arithmetic, their benefits must be $17 trillion less than the total tax they pay.

Now markets can be risky -- but it takes a government to guarantee today's workers will lose money on their total investment over a full 60 years!

This *negative* forced return from future SS must be considered in when proposing any "solution" to its problem. In fact, "who will eat the $17 trillion loss?" *is* the fundamental problem of SS, which all proposed reforms dance around without mentioning it explicitly.

Third, IMHO, private accounts could have been a big help to SS and the fiscal health of the USA post-2030 if adopted back when first seriously proposed, around the time of the SS Advisory Commission of 1994.

But too late now.

Jim Glass writes:

Erik Falkenstein has interesting data and charts relating to Feldstein's column and long-term stock returns.

John Fast writes:

Let's look at someone who makes $1000/year when they start work at age 18, and that salary increases by $1000 every year until they are making $50,000/year at age 67, and retire.

Let's assume they have a 15% payroll deduction, which is put into a fund with 3% annual return.

It looks to me like they will have $340,000 in their account when they retire, which will provide them with over $20,000/year without touching the principal.

That sounds a lot better than current Social Security benefits.

Jason writes:

I think the proof is correct, but it does not imply that expected stock returns cannot be greater than the growth rate of output indefinitely.

You can think about the Gordon growth model.

R=dividend yield+G

Expected stock returns equal the dividend yield plus the expected growth rate of dividends. For a long run steady state view like you are trying to argue, the Gordon growth model is good enough.

You are essentially saying G, the growth rate of dividends is bounded by the real economy. I think this is true. However, this has nothing to do with the level of stock returns that are sustainable in the long run.

Why? because the dividend yield can be anything, and it can be anything permanently. It depends on the price of a unit of dividend, which is a function of risk premia. If risk premia are high, dividend yields will be high and expected stock returns can be higher than the growth rate of the economy forever.

ed writes:

I am the commenter who challenged you to a bet. I agree with this new argument. I also agree (as I said before) that Feldstein's 5.5 prediction is probably too optimistic, and I have other reservations about his plan as well.

The fact remains that your argument in the previous post was faulty. Feldstein was talking about *returns.* Nothing has to grow at all for returns to be positive, not stock prices, not GDP, not even earnings or dividends.

You made some claims about the growth of "stock prices," but Feldstein wasn't talking about prices, he was talking about returns. If you were claiming that stock returns can't be higher than GDP growth, that is wrong. Or, if you were claiming that share prices can't grow faster than GDP growth, that is both wrong AND beside the point, since Feldstein was talking about stock returns, not stock prices.

If you'd like to clarify your claims from the previous post, perhaps I'd still be willing to bet you based on those claims. If you are not willing to bet based on those claims, you might want to think about retracting the claims, rather than just making some new claims and moving the goalposts.

PS - I enjoy the blog a lot, just not that particular post.

Jason writes:

Imagine two hypothetical economies.

Real GDP per capita and real dividends per capita both grow at a constant rate of 2% per annum. Current Real GDP per capita is 100 and dividends are 50.

Now in one economy the price of a claim to all future dividends is 1000 and in another it is 2000.

In the first economy the return in the long run is
R=d/p+G or 5%+2%=7%.

In the second economy the return in the long run is
R=d/p+G or 2.5%+2%=4.5%

In both economies stock prices, dividends and GDP all growth at a rate of 2%. Thus, long run returns on stocks are higher in one economy even though stock prices grow at the same rate as GDP.

Jim Glass writes:

In the real USA corporate profits have been pretty steady at around 7% of GDP for the last 70 years. (See the link in my comment above.)

That answers a lot of questions. No growth faster than the economy through compounding returns. The number of shares those profits are divided among determines earnings per share. Changes in the discount rate determine market valuation and p/e ratios.

If the future resembles the past, dividend rate of return exceeding the growth rate of the economy will always be possible -- but market valuations growing faster than the economy indefiniely will not, as profits stay at an even level in the economy. (Again, the difference being between simple interest and compound interest).

Caveat: That, of course, is with the fairly closed-economy investing opportunities of the long-term past. Today the S&P 500 earn a great deal of their profits abroad (about half, IIRC). Most of that comes from other mature economies growing about as fast as the US, so it doesn't make much difference for this purpose.

But if major new int'l "growth funds" traded in the US come to tap in a major way into China/ India/ Asia when growing much faster than the USA, the future could be different than the past.

A dude writes:

there are many ways to frame the answer, but my favorite is this:

If more is allocated to stocks the aggregate cost of risk taking (risk premium) in the economy goes down, this acts as a subsidy to enterpreneurship, and likely increases GDP growth. How that higher GDP growth is allocated between labor, enterpreneurs and stock owners is another matter.

If SS contributions are diverted to stocks, less financing is available to the government, raising the cost of treasury debt, and reducing governemnt share of the economy, thus increasing GDP growth.

Steve writes:

Arnold,

Your theory talks in gross terms. The commenter was talking in percentage terms. If:

1. Gross shareholder returns represent only a small fraction of gross national product, and

2. A high portion of gains in gross national product accrue to shareholders, then

The percentage growth in the stock market can exceed the percentage growth in national product. Obviously there is still an asymptote we reach; at some point equity growth slows down to growth in national product in percentage terms, but so long as we are still in a scenario where shareholders only receive a small fraction of the national product then we could have a long time to go before the asymptote is reached.

Elvin writes:

Corporate profits as measured by the BEA have grown at a rate nearly identical to nominal GDP growth. From 1959 to 2010, I measure the growth rate of corporate earnings at 7.0% and nominal GDP at 6.9%. Profits are also more volatile than than GDP growth.

On the other hand, earnings as measured by the S&P for the S&P 500 have grown at a rate below GDP growth. Since 1959 I measure this growth rate at 6.4%. The problem with working with these numbers is that they are incredibly volatile and the long run growth rate is very dependent on beginning and ending points. For example, after the horrific write-offs of 4Q 2008, one would have concluded that long run S&P earnings have a negative real growth rate. But earnings have rebounded rapidly and are starting to approach the nominal growth rate of the economy in the long run. Based on projected earnings for the rest of this year, I estimate the long run growth rate of S&P earnings will be 6.8%, which is pretty close to the 6.9% GDP growth rate listed above.

Thus, based on first principles and historic data, it is reasonable to assume that nominal earnings growth in the long run should be equal to nominal GDP growth. Maybe you want to include other factors--earnings from abroad or per capita adjustments--that is fine, but the starting point should be nominal GDP growth.

mark writes:

I note that your first point assumes away one of my main criticims of the earlier post, namely that US citizens can invest in non US equities and also that US equities can reflect non US income.

I agree with those who observe that this bet is different from the earlier post's thesis which was focused on equity returns, not income, and that equity returns are different from the income of the underlying business. I note that if an entity's interest rates are lower than 5.5%, then it is possible for the entity's shareholders' returns to exceed 5.5% for an exceedingly long time,, even if the entity generates no more than a 5.5% total return on investment, and logically the senior ranking of debt could cause that to occur. It is also possible for investors to find those stocks and abandon others.

Last I note that a bet with an infinite time horizon is neither winnable nor losable.

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