Arnold Kling  

Private Accounts Can Save Social Security (????)

Open Borders and The Walkin... Notes From the Field...

Martin Feldstein writes,

With a 3% payroll deduction, someone with $50,000 of real annual earnings during his working years could accumulate enough to fund an annual payout of about $22,000 after age 67, essentially doubling the current Social Security benefit. That assumes a real rate of return of 5.5%, less than the historic average return on a balanced portfolio of stock and bond mutual funds.

Mark Thoma points, but indicates skepticism with a (???). My skepticism runs to 4 question marks. I wrote in 2004 in an essay in favor of privatizing Social Security that what I called the "stock market scenario" is bogus.

The stock market scenario assumes that the stock prices will grow faster than the economy forever. This violates Stein's Law, which says that anything that can't go on forever, stops.

As I explained in the essay, the ratio of stock prices to GDP can be thought of as the product of the price/earnings ratio times the ratio of earnings to GDP. At least one of those ratios has to rise in order for the ratio of stock prices to GDP to rise.

The ratio of earnings to GDP varies depending on the state of the business cycle and on the tax and regulatory environment, which can affect the extent to which people use public corporations as an investment vehicle. (I mention that because some economists think that the public corporation is in decline, due to Sarbanes-Oxley and other assaults.) In any case, the ratio of earnings to GDP certainly has an upper limit.

The main reason that stock prices have risen faster than GDP historically is that the price-earnings ratio was at very low levels a hundred years ago. It has risen gradually since then, although the rise in P/E suffered major interruptions in 1929, 2000, and 2008. In any event, this ratio, too, has a limit.

This means that the growth in stock prices has an asymptote, which is the growth rate of GDP. Unless we approach the technological rapture known as the Singularity (and if we do approach the Singularity, that in itself will eliminate all worries about Social Security, Medicare, and much else), real GDP growth will be closer to 3 percent than to 5.5 percent. In which case, it would be safer to assume stock returns closer to 3 percent than closer to 5.5 percent.

Comments and Sharing

COMMENTS (41 to date)
Phil writes:

Does it really matter if stock prices rise relative to GDP? If the typical P/E ratio is 15, that means you're earning 7% regardless of what the stock price does.

Of course, if everyone rushes into stocks, the P/E goes up. But, still, a real return of 5% seems reasonable, no?

John writes:

"The stock market scenario assumes that the stock prices will grow faster than the economy forever."

Which economy are we talking about? The US equity markets have been doing better than the underlying US economy for a couple of years now. Why? Because the main companies driving the indices are doing more and more business outside the US than within it.

Matt writes:

Maybe this is silly but, growth beyond GDP should be possible if companies are leveraged.

If I buy a house and with 20% down, and prices rice 3%, my increase is 12% greater than my initial investment.

So how does the fact that companies raise significant funds through bonds affect their earnings? IF a company is leveraged 4 to 1 like me than wouldn't their earnings be greater than GDP growth?

JFA writes:

Which stock prices are you talking about? NASDAQ, S&P, the Dow?? Could it be that the "stock market" in 2010 includes the stocks of different companies than the "stock market" of 1950? I imagine that any index looks quite different over time, with the more valuable companies replacing the less valuable companies. Your point would seem to hold only if the profitability of companies in general will decrease as we continue towards the future, but that would characterize you as a pessimistic version of Tyler Cowen. If more valuable companies do not replace less valuable companies in the stock indices, then the stock indices do not represent balanced portfolios and you are talking past those you are critiquing.

john42 writes:

I was about to post a comment to the effect that it amazes me that Feldstein could get such an obvious thing so wrong.

But then I read the comments here by people who are similarly confused.

Guys, the concept is not difficult. If everyone in the US invests their savings in the stock market, then they simply cannot grow their savings faster than GDP for any significant period of time. This is obvious. In the same way that it is obvious that you cannot make a perpetual motion machine, but still confused people keep suggesting ways to do it.

Dan writes:

Most companies in "the" stock market (S&P 500 or DJIA) generate a significant and increasing proportion of sales internationally. Thus, under your logic, the "market" will increasingly track global GDP growth.

One could make an argument that P/E ratios are too low relative to yields, as well. With BAA yields at 4-5% ish, that implies a 20-25 P/E ratio without growth. Yes, stocks should carry a risk premium, but so should bonds (stockholders can and do hurt bondholders). In aggregate, that risk premium is a function of expected permanent losses. With a P/E ratio of 15, and nominal earnings growth of 5%, that suggests an equivalent yield of 12%, or a risk premium of 7% (????) to the BAA.

Justin writes:

Remember there are also dividends. If real stock prices track real GDP growth, a dividend yield in the context of 2-3% would get the total return to 5.5%.

mark writes:

I am not a fan of privatized SS, but do note that a) one can invest in equity markets growing faster than the US, so neither "the economy" and the "stock market" are limited to the US, b) due to survivorship bias, foreign capital infusion and other factors that need not be named in detail, it is possible for a country's "equity market' to grow faster than its "economy" for a long period of time, and c) the lower the interest rate on debt, the higher the equity capitalization ratio tends to be, ceteris paribus. Last as an anecdote, my firm has a pension plan with a 5.5% assumed rate of return which, fortunately, we have managed to achieve such that it is fully funded.

Floccina writes:

Excellent post. I agree. It has been a thought to me for a long time now that stock market growth should gradually slow. That is why I think people are better off making investments closer to home like investing energy saving devices (new air conditioners more insulation) which over the life time of the product have higher yields. The other thing people should do is to paying down loans which have the overhead of collections which means efficiency gains.

B writes:

This idiosyncratic past cannot be extrapolated into the future.

Did Arnold inadvertently claim to explain away the equity premium puzzle?

TomB writes:

I agree with JFA. The market indexes are changed to have more representative companies. As a an old company becomes less important, or less successful, a new company is added to replace it. E.g., GM and Citibank were dropped and Travelers and Cisco were added; Goodyear, Sears Roebuck, and Union Carbide were dropped and Microsoft, Intel, and Home Depot were added.

So at any point in time, the market indexes may represent the average of all the above average companies, instead of the average of all companies. Or maybe just the average of the top 75% of all companies. In any event, it is possible for the growth of the best or better companies to exceed in perpetuity that of the economy as a whole.

Yancey Ward writes:

Your future consumption can only be produced in the future; and that product of the future must be shared with the people who are still working at that time; and that rough sharing ratio has been pretty damned consistent over long periods of time (in other words, it is unlikely to change much in the favor of owners of capital).

GDP growth consists of real productivity increases of workers and increases due to growth in population. I think it proper to subtract out any GDP growth due solely to population growth. The investments of today, as a whole, will likely only have real returns equal to productivity increases over time.

Yancey Ward writes:


It is true that the indexes change over time, but investors still own the failing/shrinking companies that fall out of them. In other words, the indexes change, but the investors still have to recognize the poor performance of all the companies that are and were a part of it.

honeyoak writes:

Arnold, i would have to disagree with you on this. in aggregate stock prices relate to the marginal return to capital, not the underlying cash flows as in Modigliani-Miler. ceterious is not paribus,as increases in savings among household can be countervailed by decreases in savings for government and firms. This is why stock prices only correlate with GDP growth for unexpected changes in the economy. That being said, you are correct in pointing out that there is little reason to suppose large returns to savings over the future.

ed writes:

First of all, it is perfectly possible for assets to generate positive real returns even with no economic/GDP growth at all. This should be obvious.

Second, "returns" are not just "stock prices," they also include dividends.

Third, "stock prices" can grow without any earnings growth at all, due to share repurchases. In the past decades share repurchases have been a bigger source of returns than dividends.

What IS true is that the aggregate P/E ratio can't grow faster than GDP forever. But this statement puts no limit on steady state returns.

(FWIW, I also think 5.5% real returns is a bit too optimistic.)

Philo writes:

You shouldn't pretend to know what the future growth rate of GDP will be. Prehistorically, and through most of history, it was everywhere much less than 1% per annum; in the nineteenth-century U.S. it was less than 2%. Nowadays 3% seems a reasonable objective for the U.S. (though Tyler Cowen warns of "stagnation"). But China is doing much better than that, and very probably so could we, with better policies here and worldwide. We're doing better at growth than our ancestors did, and maybe our descendants will do even better.

Chris Koresko writes:

If we think of the GDP as the sum of private-sector and government-sector contributions, then it seems that privatizing Social Security is tantamount to shifting real investment from the public to the private sector. If we assume that the private sector produces higher returns, is it plausible that the resulting increase in GDP could produce the benefits being attributed to the high growth rate of the stock market?

ed writes:

Would Arnold be willing to make a bet? I will bet any reasonable amount of money that total returns on a US index fund will exceed GDP growth over the next 20 years.

Charles R. Williams writes:

5.5% returns on stocks in perpetuity can be consistent with a 3% growth rate in output(and equity capital). The reason is that all of this 5.5% return is consumed over the lifetime of individual plan participants. The 5.5% is reinvested only during pre-retirement years. In retirement the whole return and some portion of prior returns are consumed. So the total plan balance across the entire population is a function of demographic factors, labor force participation, wage incomes, and returns on invested capital. The system could be stable over time.

I do think a 5.5% real return on a portfolio of paper assets is unrealistic.

Lord writes:

The total return is dividends plus dividend growth. Dividend growth will slow with a slowing population but will still grow with productivity and productivity should grow somewhat faster with slowing population due to more investment in human capital but not enough to counter a slowing population. It is really that faster international productivity and population growth that will support higher returns for some time yet but it will fall over time.

The big problem with this is even if you can obtain that high a return, you cannot withdraw at that rate due to volatility. The safe withdrawal rate has been around 4% and a declining return will only reduce that further. As a result, you would need between 2-3 times as high a savings rate to replace that much income or retire later to reduce the length of retirement.

Arnold Kling writes:

My analysis would suggest that there is a 50-50 chance that the market will grow faster than GDP. So I am not psyched to bet against the proposition that it will grow faster.

Feldstein implies that the market will grow more than 80 percent faster than GDP. That is, if GDP grows at 3 percent, the market will grow at 5.5 percent. I am psyched to bet against that.

ed writes:

Ok, I will give you odds, or I will bet on GDP growth plus 0.5%, or we can adjust the returns to remove the change in P/E ratio.

I think you are wrong. Is there any bet you are willing to make?

David R. Henderson writes:

Nothing that Arnold wrote above is inconsistent with the idea that returns on an index could be above a measly 0.5 percentage points over real GDP growth. A bet I will take with you, with even odds, is that returns on the Vanguard Total Market Index will not average more than 1.2 percentage points (thus, consistent with Arnold's closer to 3 than to 5.5) above real GDP growth. The problem is that we won't know until 2031, by which time I might not be here. :-(

Joel writes:

How do dividends figure into this? If stock prices grow at 5% nominal with 2% inflation, and you have a 2.5% dividend yield, doesn't that result in 5.5%?

ed writes:

I believe to a first approximation, if P/E is constant, then:

Return = payout ratio + aggregate earnings growth

Where payout ratio is dividends plus share repurchases.

I agree that earnings growth cannot be permanently higher than GDP growth, and might be lower. But the payout ratio is not negligible. Dividends are around 2%, and share repurchases are similar, so the payout ratio is on the order of 4%. (Note that per share earnings growth will be higher than overall earnings growth if there are net share repurchases.)

I say this is HIGHLY likely to be well above GDP growth. (The other component of returns do to P/E growth or contraction is harder to predict, and will often reverse over time, which is why my bet would not be a total sure thing. It would be better for me if we adjusted the bet somehow to remove this component of returns.)

In any case, I think Arnold's argument is fundamentally flawed, and I'm interested what, if anything, he would be willing to bet on.

ed writes:

To clarify my previous comment, by "payout ratio" meant value of dividends and repurchases divided by stock price. I probably should have called it "payout yield."

Philo writes:

Even in a steady-state economy--*no* growth--the interest rate will be positive. So there will be a positive return on investment, which compounds over time.

mark writes:

Further to my earlier comment, I'd like to note that as GDP includes a large chunk of government spending - at cost - GDP is not wholly representative of private sector growth; thus the the growth rates for GDP and the equity market, which functions as a proxy for private sector ownership, could diverge materially.

ed writes:

David Henderson,

If you buy Arnold's argument, then a bet at even odds on GDP+0.5% should be unfair in your favor. The fact that you require a premium of 1.2% and STILL demand even odds seems to show some lack of confidence on your part.

Nevertheless, since I think the premium will be closer to 3%, I would gladly take your bet. Or alternatively you could explain to me why my argument in my 4:13PM comment is wrong, i.e. why Arnold is right to ignore payouts.

John Maxwell writes:


Don't payouts like dividends and stock repurchases come out of current earnings? It seems like you are counting them twice.

David R. Henderson writes:

I buy Arnold's argument. I'm a literalist. He said it should be closer to 3 than to 5.5, not that it should equal 3. 4.2 is closer to 3 than to 5.5. He said that it can't go on forever above the growth of GDP. I won't be around forever. :-( 20 years is not close.
Bet $100? Not that anyone is going to remember it in 20 years.

ed writes:

John Maxwell-
No, I am not double counting. I'm just counting payouts, and assuming that payouts will grow at the same rate as earnings (i.e.about the same as GDP).

Jim Glass writes:

The stock market scenario assumes that the stock prices will grow faster than the economy forever. This violates Stein's Law, which says that anything that can't go on forever, stops.

Stock prices can indeed grow faster than an economy forever.

Total stock valuation, (and income to stock owners that drives that valuation) can't grow faster than the economy forever -- but that's a big difference.

Stock prices can rise even while total stock valuation falls, if enough shares are redeemed and dividends cashed out.

The historical 6% return to stocks is simple interest, not compound. People have always consumed a lot of their dividends, keeping growth of stock valuation in line with growth of the economy.

There's no logical reason why this couldn't continue forever.

Elvin writes:

Ed is right. I'm surprised at how many people here are forgetting the dividend discount model. Absent P/E effects, the stock return is dividend growth + dividend yield. (And with some simplifying assumptions, it's earnings growth + dividend yield.) Thus, equity returns should be above GDP growth by the amount of the dividend yield.

One way I look at it is that equity returns are above GDP growth and bond returns are below GDP growth. The two together match GDP growth. To grow above nominal growth with stocks, investors have to bear more volatility than economic growth (earnings and the P/E effect are highly volatile). To have lower volatility with bonds, investors have to suffice with a return below nominal growth. I'd guess that Bill Sharpe has some simple theorem demonstrating this. In this sense, Arnold is right: the aggregate gains of the capital markets (stocks and bonds) is probably around the growth rate of the economy.

When we look across broad swaths of history and countries, equity returns have consistently been around 5.0% in real terms. Think of it as 2.5% real growth + 2.5% dividend yield. 5% real returns are not unrealistic, unless you think the great stagnation will get worse.

ed writes:

Thanks Elvin.

One thing, you shouldn't ignore share a source of payouts they have been much larger than dividends over the last couple of decades. Together they are much larger than the 2.5% yield in your example.

(One complication, however, is whether the repurchases are timed right. For example, buybacks were more than twice as high in 2007 as in 2009 (oops!!). To the extent that firms foolishly repurchase more shares when P/E is high, this will cut returns. Of course a savvy investor could always undo this effect in her own portfolio.)

Lance Paddock writes:
Absent P/E effects, the stock return is dividend growth + dividend yield. (And with some simplifying assumptions, it's earnings growth + dividend yield.)
Elvin conceptually gets it right, however, Arnold wins on the outcome for another reason, because he is wrong on his assumption. Real Earnings do not equal GDP growth over time. They are significantly less.

Historically real earnings growth has averaged about 1.5% and real dividend growth (more important in reality) about 1.1%. This really makes sense because of two things. First, per capita growth is probably more relevant than aggregate GDP (which has been about 1.8%) then one would expect that public equities would grow slower than the broader economy since they are established and large.

A generous long term view of real returns then is 1.5% plus the dividend yield which adjusting for repurchases can optimistically be put at about 2.3%. That equals 3.8% real.

In reality I would ignore repurchases since over time they are offset by share issuance and the benefit of share repurchases is they supposedly result in higher dividends per share in the future, which has not materialized. Still, no reason not to be optimistic.

I am surprised at how many people in the comments above assert theoretical arguments about what returns, earnings and other factors are, when the information is readily available. The numbers above are the numbers. Opinions about what earnings growth will or should be seems to be placing faith in one's reasoning over experience and evidence from which to reason.

ed writes:

Lance Paddock,

I suspect you are a bit too pessimistic about some things, but I agree with your conclusion (contra Arnold) that real stock returns will be well above real GDP growth. (3.8% is a lot better than 2.5%.)

Where are you getting the 1.5% earnings growth number? My numbers seem higher (looking at S&P500 earnings since 1960, I get more like 2% or 2.5% depending on how you measure, what period, etc.)

I'll have to think about your dim view of share repurchases. Perhaps my view of them is too rosy.

Less Antman writes:

On economics, I bow to the wisdom of Kling and Henderson, but as a money manager, I believe I have a better understanding of the present issue.

Ed is right. Total return is not the same as the growth rate, unless consumption is zero, in which case everyone drops dead.

Assume no cycles, no inflation, no new companies, no new shares issued by existing companies, no change in PE ratios, every company sells at book value, and no leverage. Let's say the profitability of every company is 6% of equity each and every year, and that every company pays out half of its earnings, which by definition is consumed by the investors, since there are no new companies or shares in my example.

Result? The growth rate of profits is going to be 3% forever, and the total return on stocks is going to be 6% forever. The growth rate in GDP is the GROWTH RATE of product. It is NOT the TOTAL PRODUCT.

In numbers?

You invest $1,000 and earn 6%, or $60. You spend $30 and reinvest $30. Next year, you have $1,030 invested and earn 6%, or $61.80. Your earnings grew by $1.80/$60.00, or 3%, but your rate of return was 6% in both years.

Stock returns will exceed GDP growth in any society whose people consume any of the production. The growth in GDP is effectively the FLOOR on returns, not the ceiling.

In the past, we could explain the difference in terms of dividends, but in recent history, dividends have been increasingly replaced by stock repurchases, which are still cash distributions to shareholders even though they aren't reflected in the dividend rate. Nonetheless, the point is that GDP growth is not the limiting factor on total return, because it ignores consumption. There isn't a single country in history whose stock returns over time were comparable to the growth rate in GDP.

Walt French writes:

Thanks, @Arnold, for the splash of arithmetic reality that so many of us would ignore (accustomed as we are, to look at our chance to gain share versus the size of the pie).

A supporting point that I haven't seen mentioned above is that we keep pouring additional capital into equities; it's therefore unsurprising that aggregate earnings rise, even if many of those marginal IPOs are doomed to be the next Pets.Com.

I am unsurprised that we over-invest in equities, just as we have over-invested in real estate: consider the choice of taking $300K and funding 5 years in med school, versus buying an apartment building (10% down) and flipping your way to become the next Donald Trump. In the first case, you'll pay top marginal tax rates; in the latter, low cap gains rates— doubly sweet in a low-inflation environment, even if not indexed.

Cap gains enjoy preferential treatment to income at least partially on the premise that investment capital is hard to come by in this society. (It's pretty hard to argue that we gain social benefit from penalizing income related to advanced education.)

But tell that to Rand Paul: he's telling all who will listen that we are awash in excess liquidity, and as far as our recent bubbles are concerned, it's hard to argue with him. Unless we do your sort of accounting, we'll badly misunderstand the real marginal return on our resources, and how to provide the best opportunities for the most Americans.

Mark writes:

You can't compare the return on the S&P 500 to real GDP; the appropriate measure is nominal GDP.

The quarterly percentage change in the S&P500 since 1950:I is 1.76%, while the comparable figure for nominal GDP 1.64%. In fact, the natural log of the two series appear to be cointegrated. However, as David Henderson points out, you will have to wait 20 years to settle the bet.

Philo writes:

Current U.S. GDP growth is constrained by the low rate of savings (partially compensated for by investment in the U.S. from foreign sources). Faster GDP growth could be achieved through higher levels of savings and investment, which would be achieved by ending (privatizing) Social Security. (Another help would be an increased willingness to accept risk.)

Historically investors have been able to get returns higher than the rate of GDP growth, because their saving (and risk-taking) has been partially offset by others' dissaving (and others' declining to accept risk). This would continue to be the case even if Social Security was terminated; there would still be younger people who were temporarily borrowing for consumption (or for investment in their own human capital, which isn't usually counted as "investment"); and there would still be retirees systematically drawing down their savings. Those who are saving and investing domestically (and accepting risk) get a disproportionate share of future GDP.

Comments for this entry have been closed
Return to top