We have been following the intellectual struggle between Paul Krugman and the Council of Economic Advisors. The basic question - can the US stock market continue to produce high returns even in a (projected) period of reduced growth? The CEA says yes; Krugman says no.

I have spent too much of my time and my reader's patience explaining how the seeming conflict between "return on capital" and growth" can be modeled in the macroeconomic framework employed by the Social Security Trustees.

However, thanks to a very illuminating comment from one of my readers, and drawing on inspiration from Andrew Samwick, I can now resolve the puzzle in a more traditional framework of dividend yield and P/E ratios.

Let's set the stage - folks have been saying, in effect, the following: historically, the US GDP has grown at 3.5% per year, and stocks have had a dividend yield of 3% per year;

profits (net of depreciation) have grown with the economy (and kept a relatively stable share thereof), so, on balance, stocks have produced a real return of 6.5%, composed of 3% dividend yield, and 3.5% capital appreciation, also known as capital gains.

However, folks go on to say, the current yield is (roughly) 1.5%; future growth is forecast to be 2.0%; therefore, we have a problem - if the return on capital is 6.5%, and 1.5% is paid out in dividends, that leaves 5% to be reinvested. Let's allow 1% for stock buybacks, and we are down to reinvesting 4%. But if we reinvest (i.e., expand the capital base) at 4%, then profits will grow at 4% while GDP only grows at 2%, and the profit share of US corporations will become an absurdly high proportion of the US economy. (Here, "absurd" is based on historical evidence, or common sense - over 75 years, a 2% growth differential results in a profit share rising from, let's say, 10% of GDP, up to 44% of GDP. This is grand news for Bill Gates's heirs, but a bit rough on the rest of us.)

So, folks conclude, since that future world is not plausible, the starting assumptions must be wrong. But where? The growth forecast is pretty reliable (based on things like a demographic projection of the workforce), and the dividend yield has an eighty year history behind it. Aha! It is the rate of return number that must be suspect. The world has changed, these people say, and the future rate of return must change with it. Lower growth, lower returns, night follows day, autumn follows summer, this is the way of the world, and the sun is setting on the US equity market.

Or, somewhat more gloomily, we could have a stock market crash, stocks could start over at greatly reduced prices, and we could march forward with high returns from the new, lower starting point. But from where stocks are priced now, hopeless!

That, anyway, is the theory as I understand it; if someone would care to guide me to a concise description of such a view, we live to learn.

And we beg to differ. Let me start with a question - does your model have HAIR? That would be a Hidden Assumption of Impossible Reinvestment - maybe, in your model, you are simply putting your capital in the wrong place.

Let's switch gears for a moment. Imagine BigCo has capital equal to 1% of GDP, and provides a 20% return on capital (this must be a huge private equity deal, or folks would bid the price up and the yield down instantly). My question - can BigCo produce this 20% Return on Capital for the next 30 years?

Some quick noodling tells you that if BigCo grows at 20% while GDP grows at 2% for thirty years, BigCo will grow by a factor of 237 while the economy increases by a factor of 1.8; from its humble origins, BigCo will swamp the US economy.

You, a skeptic, tell me it is impossible. I salute your facility with exponents. But you failed - BigCo may well be able to deliver a 30% Return on Capital for thirty years, or forever (absent competitive forces, but don't let's get distracted).

Why? Your model has HAIR - you made a hidden assumption that BigCo would reinvest all of its Profits (i.e., return on capital) back into the capital base. As the capital base grew, the profit target grew, and thirty years later, both the profit and capital figures were absurdly high as proportions of GDP.

But why did you assume that? Suppose BigCo pays out *all* of its profits as dividends. Then the capital base does not grow, the annual profits do not grow, and BigCo is actually on its way to becoming SmallCo -as GDP grows, BigCo becomes a *declining* share of the US economy.

Hmm. A 20% return on capital for thirty years with no growth, and it does not swamp the US economy. Well, if you allow BigCo to pay out dividends, this will work fine.

So, where is the HAIR in our earlier model, with 2% GDP growth, a 2.5% dividend yield, and a 6.5% return on capital? Well, remember we agreed that the problem with the model was that profits grew to become an unrealistically large number? We solved that by lowering the rate of return, but we might just as well have raised the dividend yield.

Suppose we had. Let's picture MyCo with a starting capital of $100, and a return on capital of 6.5%. First year profits are $6.5; since the economy will only grow at 2%, let's reinvest 2%, or $2, to expand the capital base at that rate. The rest, $4.5, is paid out as dividends.

Next year, the GDP will be 2% larger; since my capital base is 2% larger, my profits will also be 2% larger, but they will be the same proportion of GDP as previously. If we continue to pay out a (slightly higher) dividend, and grow the capital base by 2%, we can keep this up forever. The return on capital will always be 6.5%; the profit as a percent of GDP will not change; and no one will have a problem.

Well, yes, some will have a problem - "isn't that dividend yield awfully high by historical standards"?, someone will ask. Well, yes. But I have a quip, and a serious answer. Quip first? Dividend policy, like the Constitution, is not a suicide pact. If companies really don't have any suitable investments available in a low growth economy, it is a bit odd to assume they will invest anyway. The historic dividend yields reflected a certain historic growth pattern; let the new yields reflect the future!

In a closed system, I think that answer would be compelling. However, Jim Glass has his hand up, so let me address his point. This will also reassure those who are desperate to maintain a low dividend yield.

Why did we feel obliged to increase dividends? Because we wanted to grow the company's capital base (and profits) in line with the growth of the US economy. But isn't it a big world out there? Is there some reason that the company can't invest its capital abroad?

Suppose it does. Imagine that MyCo has $100 of capital, initially all in the US. It earns $6.5 as before, reinvests $2 in the US as before, but only pays out $1.5 as dividends, for a 1.5% yield. This leaves $3. In our original "implausible breakdown" model, this went back into the US, resulting in an implausible level of capital and profits. But let's invest overseas.

So, year 2: MyCo has *US* earnings and capital in line with *US* GDP. No problems - US capital and profits are growing at 2%, in tandem with the economy.

However, a tiny new item appears on the MyCo report - foreign profits of (6.5% x $3) or $0.20.

And from tiny acorns, mighty oaks grow - depending on what one assumes about the reinvestment of foreign and domestic earnings, the foreign side of MyCo will become quite large - in my quick spreadsheet, with dividends paid on both US and foreign capital, reinvestment in the US to keep pace with GDP, and all "excess cash" available after dividends to be reinvested abroad, in 20 years the US capital of MyCo is $148.59, while the foreign capital is $116.74. (The $148.59 simply reflects 2% growth, obviously).

Now, does this approach lead to a train wreck of implausible proportions? Not if the world economy grows by 4.5%. And if it does not, then we fall back to increasing the dividend yield. Although the total profits of MyCo grow relative to US GDP, the US share reported in GDP accounts does not. This should be a stable, plausible scenario.

Now, obvious caveats - these numbers and examples do not, and can not, *prove* that the US stock market is correctly valued, or that the dividend yield must remain at 1.5%, or that foreign investment by US corporations *must* grow to some number by some date.

However, what these numbers *do* prove is that a perfectly coherent, mathematically consistent explanation of current share prices, earnings yields, and dividends yields is available. Toss in foreign investment, and we offer this in refutation of the various "HAIRy" models that attempt to "prove" that stocks must fall.

Folks who would care to vex me are encouraged to bring over some gloom and doom proofs of impending economic calamity, and we will see if we can spot the HAIR on them.

Thanks very much. I promise my (few remaining) regular readers - we are almost off of this, and we look forward to resuming our regular ranting.

And yes, I still want the Dean Baker "No Economist's Left Behind" Cup. You haven't seen the end of me!

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