"The Bank of Canada should peg the TSE 300" - revisited

"The Bank of Canada should peg the TSE-300" is the title of a Carleton Economics Department working paper I wrote in 1992. (Sorry, but no web version available; this was in the olden days when all we had was paper, and when the TSX was the TSE.) Given the recent turmoil in financial markets, and the renewed interest in having central banks look at asset prices, I was wondering whether to resurrect this paper, but dithered. Now Roger Farmer has beaten me to it. Mark Thoma posted it on his blog, and Tyler Cowen on his.

The reactions in the comments are mostly either unfavourable, or incredulous. I thought I would write a few words in defence of the idea, and then say why I no longer support it.

Many critics are just confused, and think that using monetary policy to peg an index of stock prices is some sort of interventionist policy that prevents markets finding their own equilibrium. But if governments produce money, and they do, then governments have to decide how much money to produce. They have to target something. That something can be the price of gold, or silver, or the exchange rate with another government's money, or the CPI (as in inflation targeting). Or it can be an index of stock prices. In principle, any nominal (measured in dollars) variable can be the target for monetary policy, and the TSX 300 is a nominal variable.

Pegging the TSX 300 is no more interventionist than pegging the price of gold, or pegging the CPI (as we do now with inflation targeting). In the long run, market forces determine the real (inflation-adjusted) value of the TSX 300 even if the Bank of Canada pegs the nominal value; the same is true if the Bank of Canada pegs the price of gold. If this bothers you, just think of the Bank of Canada pegging the value of the Canadian dollar to the TSX 300, rather than vice-versa.

Let me be more precise. My 1992 proposal was that the Bank of Canada should peg the time-path of the total return index of the TSX 300, so it would grow at some fixed rate of (say) 7% per year. The total return index is a better target then the index itself, because it is immune to arbitrary changes in firms' dividend payout ratios.

There is one very curious effect of pegging the total return index to grow at (say) 7% per year. It would mean that a stock index fund would be as safe an investment as Canada Savings Bonds are now, since the holder would be certain of the nominal interest rate (but the real interest rate would be uncertain in both cases). It would be hard to imagine that the equity premium could persist, which could be an important advantage of the policy. All nominal interest rates on government bonds and other safe assets would have to pay the same 7% per year. The TSX 300 would be an ideal investment for widows and orphans.

The main rationale for the policy would be the hope that it would tame financial bubbles and crises. Also, if stock prices predict the business cycle, and if this correlation implies causation, taming stock prices might also tame the business cycle.

It seemed to me a good idea in 1992, but this was before inflation targeting really got off the ground, so I didn't have much to compare it to. A few years ago, when inflation targeting seemed to be performing very well, I changed my mind, and decided it was "very interesting....but stupid". Now I am just uncertain. Here are the main problems.

First, stock prices are very flexible, but a lot of goods prices are very sticky. There is a long-standing principle in macroeconomics that business cyles are caused by sticky prices, and the best macroeconomic policy is to make sure that the prices which don't change quickly don't have to change quickly. This principle suggests we should target an index of sticky prices (or wages), and the CPI comes a lot closer to this than the TSX 300.

Second, the real fundamental equilibrium value of the TSX 300 can change by a large amount very quickly, due to fundamental changes in profitability, the growth rate of profits, or real discount rates. But if the nominal value of the TSX 300 were pegged, the only way the real value of the TSX 300 could reach its new equilibrium would be for the CPI to adjust. Big fluctuations in the CPI would be undesirable if they did occur, and even more undesirable if they needed to occur but couldn't, because goods prices are sticky. For example, a cut in corporate taxes which would cause a (say) 20% rise in stock prices when the Bank targets the CPI would instead have to cause a 20% decline in the CPI if the Bank targets stock prices.

Finally, the stock market is perhaps a barometer of the state of the economy, but we cannot be sure that pegging the barometer would stabilise the weather. Goodhart's law suggests the opposite. Perhaps the bubbles in asset prices that were suppressed would only pop up somewhere else. Indeed, the classical dichotomy suggests that they would pop up somewhere else; positive asset price bubbles would pop us as negative CPI bubbles.

I'm not prepared to rule out targeting some weighted average of goods prices and asset prices. But even a broad index of stock prices is a narrow representation of even financial assets, let alone land, houses, and human capital.

Comments

[Don Lloyd]

"...But if governments produce money, and they do, then governments have to decide how much money to produce. They have to target something...."

This is a false assertion. Money could be produced only for replacing worn existing money, with no attempt made to stablize some imaginary magical general price level. In this case there would no negative effects from monetary flow. The correct assertion is that new money cannot be produced without without inserting it in the economy at a given place and time, with its effects occuring spread over a range of elsewheres and elsewhens.

To claim that the government must stabilize price levels flies in the face of nearly a century of history in which the Federal Reserve has destroyed more than 95% of the purchasing power of the US dollar even after all of the productivity gains in the economy in the past century.

As an analogy, consider a deep mountain lake with 30 degree sides. Assume that the lake water is supplied only from rain and is drained only by evaporation. In this case an increase in the rate of rain may be countered by the increase in evaporation due the larger surface area contained within the 30 degree walls of the lake. With no artificial control of water flow, a fishing boat need not spend fuel in station-keeping against the artificial currents which no longer exist.

Back to money, the economy is dependent on relative prices, not on absolute prices and absolute monetary supply. A larger supply of money and lower monetary purchasing power are neither better nor worse for the economy than the opposite. But the existence of monetary flows associated with an increased monetary supply tend to distort relative prices.

Regards, Don

[Nick Rowe]

Don: I would describe your proposal (where the central bank holds the stock of money constant) as money stock targeting. It is just like Milton Friedman's proposal that the money supply be made to grow at a constant "k%" per year, just that you set k=0.

I think there are three things wrong with your proposal: If the economy has real growth of (say) 4% per year (and if velocity were constant on average) this would mean deflation of 4% per year. So nominal interest rates would be about zero, and we would always be in a liquidity trap. Second, velocity (or money demand) doesn't seem to be very stable over time. When the Bank of Canada tried a k% rule in the 1970s/80s, it eventually abandoned it, because changes in banking technology kept shifting the money demand curve. Thirdly, in a financial crisis, it prevents the central bank doing what's needed, which is to increase the money supply to offset a sudden increase in money demand.

I'm not claiming the Fed has historically stabilised the price level.

I like your lake analogy. Good negative feedback mechanism there. "High lake levels, more evaporation, lowers lake levels."

But the last point is exactly what is at issue. If money really were neutral in both the long run and the short run, then it wouldn't matter what monetary policy we adopt. The Bank of Canada could toss a coin every year: heads - double the money supply; tails - halve the money supply. If you believe monetary policy matters, then you must believe in some sort of non-neutrality, at least in the short run. Now, when you assert that changes in the money supply distort relative prices, you are echoing an Austrian idea. Decades ago I read a lot of Austrian economics, and liked a lot of what I read, but never could see the logic of that particular Austrian idea. If the central bank makes the money supply grow at (say) 10%, then in the long run there will be 10% inflation (ignore real growth for simplicity), and so the demand for money (in nominal terms) will also grow at 10%, so there is no affect on credit markets. All that happens is that the government/central bank is imposing an inflation tax, and the only markets that are affected are : shoeleather (more trips to the bank); the market for whatever it is the government decides to spend it's revenues from the inflation tax.

[Richard H. Serlin]

Many critics are just confused, and think that using monetary policy to peg an index of stock prices is some sort of interventionist policy that prevents markets finding their own equilibrium.

But farmer didn't just say changing the money supply or Fed Funds rate in response to changes in the stock market, he said the actual direct and specific purchase of just this one asset, the S&P 500 for example -- managing a specific price relative to other prices in the economy, not just managing the general price level without attempting to change relative prices, as is done now. Farmer wrote, "A logical extension of this idea is to pick an indexed basket of securities: one candidate in the US might be the S&P 500, and to control its price by buying and selling blocks of shares on the open market.".

He's talking about distorting relative prices

There is one very curious effect of pegging the total return index to grow at (say) 7% per year. It would mean that a stock index fund would be as safe an investment as Canada Savings Bonds are now, since the holder would be certain of the nominal interest rate (but the real interest rate would be uncertain in both cases). It would be hard to imagine that the equity premium could persist, which could be an important advantage of the policy. All nominal interest rates on government bonds and other safe assets would have to pay the same 7% per year. The TSX 300 would be an ideal investment for widows and orphans.

The severe problem with this is that risky, or very risky projects could be financed at the risk-free rate -- talk about encouraging excessive risk taking!

Obviously Farmer, an excellent economist, dropped a bomb here. This is something you'd have to be very careful with and study very thoroughly, but I could see it being ok perhaps at least in an extreme case, like market P/E over 40 or under 5. Key questions, as Mark Thoma pointed out, are when, how much, and how.

Let me offer, however, a much less radical idea that could be nonetheless effective at decreasing bubbles and busts in asset markets, and that is a warning system, like with cigarettes, based on the current market P/E ratio. Research has shown the market P/E ratio, in its various forms (10 year inflation adjusted, cyclical adjustments, depreciation adjustments, etc.) to be highly correlated with bubbles and busts, and with subsequent risk-adjusted returns, and this makes great sense as investors own the earnings. And, they by and large get those earnings, about half from dividends and half from ownership of real assets purchased with the earnings.

If brokerages simply were required to issue a prominent warning, verbally and/or in writing, on the dangers of investing in the stock market when the market P/E hit a certain level, say 35, I think, if done right, prominently enough, and promoted well by the government, this could really discourage laypeople from investing in the stock market during strong bubbles.

I teach one of the largest personal finance courses in the U.S. at the University of Arizona, and am president of one of the largest personal finance education companies, and I can tell you few of my students understood P-E ratios before I taught it, or much about the market at all. I think a good prominent warning system could be very effective.

It could be color coded, something like white when between 15 and 25, orange when 25 to 35 and red when over 35, with a strong warning of the dangers of investing with a market P/E that high (the exact numbers would depend on which form of the P/E ratio was used). On the other end of the scale, it could be light blue when 7 to 15 and dark blue when under 7; there you would have a warning against selling, and not hanging on, if feasible, for what look to be high long run returns.

Every purchase or sale would feature the color code prominently on the computer screen, in writing, etc., with appropriate warnings, before the transaction was finally agreed to. In addition, advertising on TV and in print would support the warning system's awareness and attention. Likewise, I'd like to see a warning given regarding the dangers of not diversifying every time someone purchased an individual stock, or a fund concentrated in just one sector.

[Nick Rowe]

Richard: i have to disagree with you there. If Roger dropped a bomb, then so did I!

The central bank can peg any one nominal price it likes, but it cannot peg two nominal prices, because that would mean pegging a relative price. It can, for example, peg the dollar price of plywood, but if it does that it must let the CPI adjust so that the relative price of plywood can find the equilibrium, as determined by real, not monetary forces. Similarly, the Bank can peg the CPI, or the TSX 300, but not both (at least, not in the long run).

For example, suppose the equilibrium price of the TSX300 is 10,000, given today's CPI and today's dollar earnings (of the firms in the TSX). Imagine the Bank of Canada gets it wrong, and pegs the TSX300 to 20,000. The result is that the CPI doubles, nominal earnings double, and the equilibrium P/E ratio is restored that way.

Pegging the total return index to grow at (say) 7% does have weird results, I admit. But this only means that the nominal rate of return is 7%; the real rate of return can (and would) vary. At the moment, where central banks (more or less) peg the CPI, then nominal bonds are not only safe in nominal terms; they are (almost) safe in real terms as well. By pegging the index to grow at 7%, any variance in real returns from the index would have to show up in the CPI. The equity premium puzzle suggests there is far too little investment in risky projects.

Your own proposal is more sensible (though not as exciting theoretically ;-) ). Sort of like an official financial tsunami warning!

[Nick Rowe]

Richard: On second thoughts, I am not sure if I have interpreted Roger correctly. I found this statement on his web page: "5. Provides a plan for a new institution, similar to the Fed, that would stabilize asset prices by standing ready to buy and sell a basket of indexed securities."

If the Fed pegs the CPI, and this other institution tries to peg stock prices permanently, then we have a problem.

A clever wheat board can smooth out fluctuations in the relative price of wheat. Even a not-so-clever wheat board can peg the relative price of wheat temporarily (if it's got enough cash and storage facilities). But no wheat board can peg the relative price of wheat permanently just by buying and selling wheat, unless it can control production and consumption (subsidies, taxes, output restrictions, burn wheat, give away to poor countries, etc.) Same with stock prices.

My 1992 proposal was for the Fed to stabilise stock prices, and only stabilise stock prices. That's different.

[Richard H. Serlin]

Yeah, there's a lot of weird and distorted stuff that can happen if you start trying to rigidly control the nominal return on the S&P 500 or TSX 300. Yes, the CPI could vary and this would allow the real return on stocks to vary, in which case, TIPS would become the investment of choice to try to avoid all risk. Stabilizing prices, pricking bubbles (and reverse bubbles), is of course different. As I said, I think this is something worth looking at.

I have an explanation for the "equity premium puzzle" that I have not seen in the literature. Briefly:

As we know from basic economics, all other things equal, when demand increases, price usually increases. But all other things may not be equal, especially over the long run. For example, when demand for VCRs increased in the 1980s, it allowed for greater scale in manufacturing, and a decrease in price over the long run.

All of the explanations for the equity premium puzzle I have seen in the literature are based on the demand side; trying to find utility functions for a representative investor, and ex-ante probability distributions for returns, that would explain investors demanding such high average returns for stocks relative to bonds, rather than bidding those returns down. But I suggest a supply based explanation: The long run supply curve for corporate stock may simply be extremely long and flat, and consistently about 5 ½ percentage points in return higher than the premium bonds supply curve, even at stock quantities as high as the entire national savings rate.

Why would this be? I posit that stock might simply allow a firm to create more wealth with an investment dollar than bonds, and this is because of the flexibility of stock. Firms are able to invest in high return long run projects when they raise money with stock that they sometimes cannot when money is raised from bonds due to the short run constraints of having to make interest payments and satisfy bond covenants.

With stock the firm has greater flexibility to take large projects which may make little or no money for years, which may even lose money for years, but which overall will be very high return due to long run profits. There are many areas where short run constraints (often undue ones) greatly decrease optimization. This is true of business. It's true of politics, and it's also true of academia (unfortunately, very true.).

Warren Buffet, arguably the most successful investor in history, constantly attributes his success to unusual efforts and willingness to avoid short term constraints, so that he can choose the projects, within companies he controls, and in buying stock, that offer the highest NPV (overall gain considering everything relevant, not just short and medium run profits). For example, in discussing his use of insurance company funds rather than debt to finance projects, he writes in his Berkshire Hathaway statement of business principles , "...they are liabilities without covenants or due dates attached to them. In effect, they give us the benefit of debt — an ability to have more assets working for us — but saddle us with none of its drawbacks."

If my supply based hypothesis is true, or true to a large enough extent, then we could expect to continue to see stock returns outperform bond returns by large margins over the long run.

A graph of the explanation is available here.

[JKH]

Nick,

Your post is the subject of Mark Thoma’s first post for 2009.

I think his Taylor rule application is simple and elegant, and a logical first step for this sort of thing.

But there must be as strong if not stronger case for incorporating growth in broad credit aggregates as well.

I think the effect of monetary policy on the equity risk premium is best transmitted indirectly by the central bank targeting credit conditions that may contribute to destructive equity bubbles.

Outright central bank intervention through open market operations in stock index prices seems awfully unwieldy and somewhat dangerous to me.

[Nick Rowe]

Richard: I think you are right to insist we look at the supply-side of the equity premium puzzle, as well as looking at the demand side (like everybody else). Suppose we grant your assumption that firms' supply curve of stocks is well above their supply curve of bonds. Then we can restate the equity premium puzzle as : why do bonds exist (in equilibrium)? Suppose we re-draw your supply/demand diagram, and put the debt ratio on the horizontal axis, and the weighted average cost of finance on the vertical axis. We can then restate the equity premium puzzle as: "why do we get an interior solution? Why don't the S & D curves cross at zero?

JKH: I can't think of any obvious theoretical reason why a broad credit aggregate would be a better or worse proxy than stock prices. I worry that measures of credit (nominal gross debt?) may be subject to technological changes in the financial sector like changes in the degree of intermediation/disintermediation. Credit is bit harder to measure and define consistently than a stock price index, and data is not available continuously (though the same is true of the CPI).

[Phillip Huggan]

Two different proposals. The TSX 300 is large and middle cap stocks of our industrialized economy and is overweight resources vis-a-vis the rest of industrial world. S&P 500 is large cap non-conglomerate stocks and is overweight USA consumer spending vis-a-vis world. I like the Canadian proposal marginally better than the USA proposal because their consumer spending is too much and our resources are probably a little underpriced now. But both ideas pretty much suck.
Nothing wrong with supporting some sectors of economy. AB supprots oil sands. Canada once bankrolled oil sands and most novel sectors. Everyone supports farmers. Libs and Cons support aerospace. Progressive parties and countries support Greenshift-like policies. NFLD exempt from transfers. etc. This is simply supporting large and middle caps overweight resources here and large caps there overweight consumer goods stocks. Once again, why? Why support this subsegment of the economy over others or over general revenue expenditures and federal debt. Why is this better than daycare here or universal healthcare there? What is it that this class of corporations have that makes them a good tax-payer investment?
I hope the argument isn't that since they rode the crest of boomer prime over past four decades returning 8-10%/yr, that somehow everyone who is sixty now will become 25 once these dollars flow in and GDP growth will trend towards 8-10%/yr. I'm hoping for some sort of argument that globalized companies have better access to the emerging market than say, preventing mines from being taken over when commodity prices are low. But I've yet to here any argument.

[Nick Rowe]

None of the above Phillip. It's not a question of which sector of the economy we "support". This isn't a support program. It's a question of "what do we tie the value of the Loonie to?" Do we tie it to gold, silver, the US dollar, the CPI, or to the TSX?

[Phillip Huggan]

You are looking for something revenue neutral (or starting from a small subsidy and remaining constant over long term) to smooth out business cycles or looking for something to highlight bubbles? Or both?

[Phillip Huggan]

This paper confirmed my suspicion that economic growth occurs as a result of increasing R+D: elsa.berkeley.edu/~chad/SourcesAER2002.pdf
I would suggest you peg currency printing to the global total number of new of researchers (which happens to be around 2-3% I think, what inflation is pegged at now by fluke). Or use global GERD growth (R+D spending but discounting 50% of military R+D).
Another extremely sophisticated strategy would be to measure the total return expected (including all externalities) of existing $CAD assets, by expected future returns of future spending. If returns are better (for instance Obama will spend more on healthcare and less on war than GWB, presumably), printing money 1st is okay followed by spending as printing stops. You could extend this to the sphere of all credit too by treating printing currency as credit along with mortgages, bank leverage ratios, debt interest (probably most printed money adds to federal debt on the balance sheet), expected future inflation increases, longevity decreases, etc. This is when we can start to move economics forward beyond Keynesian mopping up of bubble-induced unemployment. Globalized corporations get much of the cash and pay few of the externalities so indoctrinating them into public monetary policy is a step backwards. Coal trusts and tobacco and Haliburton do not need to grow at all.

TSX 300 tracks luxury goods spending in USA along with construction activity in China, more than anything.
Turning on the cash taps penalizes economic activity before the cash flow and comparitively rewards new spending that occurs after the cash flow. So whatever the solution is, it should measure how much better or worse the new $CAD assets are to be in comparison to past assets that are to be inflated/printed-away. If Harper's stimulus (really, the budget he lost in his sweater) is paying us all to bury dogbones, the printing presses should turn backwards as the Dogshift is enacted. But if he has a plan to take us to the land of the Jetson's and universal daycare and end AGW and end poverty, print away man. Whatever we peg the presses to should reward spending money better.

[Richard H. Serlin]

Ok, so essentially the question is why there is any debt (bonds) at all if equity allows much greater creation of wealth and therefore higher expected returns?

The answer is essentially clienteles and changing marginal costs.

First, you have clienteles of investors in reality, and this is a big problem of the method you typically see for attempting to explain the equity premium – assuming a representative investor. Because the mathematics can get extremely complicated, modelers usually assume a representative investor, with a representative utility function and risk aversion paramater(s), and then they try to estimate those parameters from historical data.

In reality, you have some investors, and investor clientelles, who are far more risk averse than others, for example the elderly clientele, and they will still purchase substantial debt (bonds), even with a far lower expected return, to get even just a relatively very modest decrease in risk. As you can see, the way I drew my graph, there is much less demand for debt than for equity, but there is still a significant amount.

Now, what about the supply, why do firms supply bonds? Because they can finance with a lower expected return, or interest, cost. It increases the expected profit to the existing owners of the firm, the existing shareholders. And, at least initially, this benefit is typically not outweighed by the cost of decreased operating flexibility. The first units of debt will have little marginal cost of decreased flexibility, but the marginal cost will tend to rise steadily as more units are taken on, at least in the short run.

A typical firm will have some good projects anyway that can be expected to safely return substantial cashflow quickly, so debt can be taken on to finance them with little or no restriction on the ability to take high NPV long term and/or riskier projects. However, as more and more debt is taken, it marginally hurts flexibility more and more.

So my explanation does not have to mean that an economy of rational people will reach an equilibrium of no debt.

Like most things in economics there is an unfortunate tendency to debate what is thee explanation, when for the vast majority of things there are many explanations, or factors, substantially leading to the phenomenon.

Certainly, there are demand side factors, and certainly there are behavioral factors – I think a big one was just ignorance and misunderstanding; most laypeople thought the risk of stocks was much greater than it really was, and the expected return was much less than it really was. But, I think it is likely that my supply side explanation is also a strong factor, and I have not seen it anywhere in the literature.

And it has important implications. First, the demand and behavioral explanations tend to lead to a conclusion that the equity premium will shrink substantially in the future. My explanation shows that it may not at all. It may even increase due to increasing returns to scale. Second, my explanation shows a way to increase long run growth, at least expected long run growth.

If empirical research utilizing my theoretical explanation shows large increases in production due to the increased long term flexibility from equity, then economic growth can be increased by encouraging stock financing. And right now there is the opposite in the U.S.; debt financing is encouraged, with the deductibility of interest.

By the way, I'm not sure the graph you mentioned is quite right or appropriate. The weighted average cost of finance, or capital (WACC), is a price to the firm, not the investor, so the demand curve would look funny, and may not shed much light. Also, on the firm side WACC is a number unique for each project. An acceptable firmwide WACC, and thus supply curve, depends on the projects taken. I'm not sure this is a good way to graph this.

[Richard H. Serlin]

Actually, I thought about your graphing further.

You have Debt/Equity on the horizontal axis. So for the Suppliers – the firms, this would be the firms' Debt/Equity ratio. For the demanders – the investors, this would be the ratio of debt to equity in their portfolios.

On the vertical access would be the, I'm assuming expected, weighted average cost of finance for the firms from the mix of debt and equity. And this is the expected weighted average return of finance for the investors from their protfolios.

So, what do the curves look like?

Demand: When the Expected WACF, E[WACF], is high, then investors will be willing to settle for more equity in return. As E[WACF] goes down, they will demand a higher and higher percentage of debt in their portfolios as compensation – the risk-return trade-off. So, the curve slopes downward. A good model would be crescent shaped, hitting the vertical axis at some point high, or very high up. It actually would never hit the horizontal axis, because we can assume that no one would invest in a corporation for zero (real) return.

Supply: Yes, this does slope in the same direction, downward also, but that doesn't mean that the curves have to intersect at D/E = 0. Supply also slopes downward because if E[WACF] is high, then, in return, firms will require the benefit of very little debt financing, or they just won't do it. And, the lower E[WACF] goes, the more debt firms will be willing to accept. At E[WACF] = 0, firms could arbitrage with U.S. Bonds, and so will be willing to go to 100% debt, or D/E = 1.

So the two curves slope in the same direction, but they almost surely intersect the vertical access, where debt is zero, at different points, with the demand curve probably much higher.

Given that the Supply curve hits the horizontal access, but the demand curve doesn't, there are two points of intersection, two candidate equilibria, both in the interior.

[Nick Rowe]

Richard: I'm trying to get my head straight on this, and keep getting muddled!

First, let's put the debt ratio (rather than the debt/equity ratio) on the horizontal axis, i.e. debt/(debt+equity), so it goes from 0% (all equity) on the left, to 100% (all debt) on the right. (I think that's maybe what you meant to say).

And yes, expected average cost of funds on the vertical axis (implicitly we are assuming a given total quantity of funds, so we don't have to draw a 3D graph).

The households' curve slopes down, since they prefer debt to equity, and would require a higher EACF to hold all equity, and will be willing to accept a lower EACF as we move right and hold more debt.

The firms' curve slopes up, since they prefer equity to debt (the opposite of households), and would be willing to accept a lower EACF to issue all equity, and will require a higher EACF as we move to the right, and issue more debt.

If there are some households who desperately want debt (because they are very risk-averse), and if there are some firms who desperately don't want to issue debt (for some reason), then we get an interior solution.

Now, let's see if we can restate the equity premium puzzle: given the market debt ratio (I can never remember if it's around 40% or around 60%), does it seem plausible that the marginal household would be risk-averse enough to be indifferent between debt and equity at the market equity premium? In other words, is the marginal household sufficiently different from the average household that representative-agent analysis gives a misleading result? Dunno.

[Richard H. Serlin]

I think this graph is hard to get right because it doesn't fit the standard supply and demand Walrusian auction mode very well. In that case, you have quantity on the horizontal axis and price on the vertical axis.

You could imagine an auctioneer calling out a price of say $1, and then seeing what quantity of the good the consumers will want at that price. Then, he calls out a price of $2, and you see what quantity they will want at that price, and so on, until you map out the whole demand curve.

For the supply curve, when the auctioneer calls out a price of $1, you see what quantity of the good the firms will want to sell at that price. When he calls out a price of $2, and you see what quantity they will want at that price, and so on, until you map out the whole Supply curve.

But one problem with putting D/(D+E) on the horizontal axis and E[WACF] on the vertical, is that when the auctioneer calls out an E[WACF], say 10%, the investors want to have portfolios with D/(D+E) = 1. When he calls out E[WACF] = 11%, they still want D/(D+E) = 1, and you just end up with a straight vertical line at 1, not a very useful curve; it doesn't shed much light.

If you are going to put E[WACF] and D/(D+E) on the axes, then it's more useful to ask not what D/(D+E) the investors will want for a given E[WACF], but which one they would just be willing to settle for, or tolerate.

Likewise, you would ask not what D/(D+E) the firms will want for a given E[WACF] – that's always going to be zero – but which one they would just be willing to settle for, or tolerate.

If you do it this way, asking what they would just be willing to settle for, or tolerate, then you get curves like I described above.

When E[WACF] is high, say, 10%, the least desirable thing investors would be willing to tolerate is something with a pretty low D/(D+E), because they are compensated for the extra risk of an equity heave portfolio with a high expected return. For firms, when E[WACF] is high, then they have to pay out a lot of money to investors, as a result they will not be willing to tolerate having too much of the financing be debt; they will only tolerate a maximum D/(D+E) that's pretty low.

So both curves will be high on the left, and if you go through similar reasoning, you see that both curves will be low on the right, so they will both slope in the same direction.

In any case, though, I don't think this is an illuminating way to graph this. In the market place, firms offer an expected return for equity, and another one for debt, not an E[WACF], and investors decide what quantities to purchase for an expected return for equity, and another one for debt.

If you imagine the Walrasian auctioneer calling out expected returns, you get a graph that I think is more illuminating, one like I drew, one which will show what would actually be purchased and at what expected returns – which is what we're really most interested in.

With regard to the actual debt ratio of the market, Ivo Welch gives a figure for U.S. stocks in his 2004 JPE article, Capital Structure and Stock Returns (not about the equity premium puzzle):

My data set begins with all publicly traded U.S. corporations from the period 1962–2000 from the annual Compustat and Center for Research in Security Prices (CRSP) files...The debt ratio, the dependent variable, has a mean of about 30 percent of firm value and a median of about 25 percent. (page 109)

So the debt ratio is not as high as you were thinking in the U.S. Generally, though, my supply side hypothesis that the supply curve may be very high, long, and flat, or even increasing due perhaps to increasing returns to scale and potential new technologies, explains the high equity premium, which is the big issue in finance, the big "puzzle". As far as quantities purchased, it's consistent with either high or low amounts of debt. To explain the actual quantities purchased, you would also look at demand and behavioral factors.

But my point is, my supply-side hypotheses are potentially very important explanations or factors in the equity premium puzzle, and I have not seen them in the literature.

[Richard H. Serlin]

I should add that with regard to your question, "In other words, is the marginal household sufficiently different from the average household that representative-agent analysis gives a misleading result?".

From my experience and knowledge, unless I had extremely rare luck in that experience, there's a very wide dispersion in the population's risk aversion. For example, old people are understandably much more risk averse than the young in their portfolio mix, and are in fact counseled by most investment advisers to be that way. A common saying is that your debt ratio should be 1% for each year of your age.

There's also a wide dispersion in perceived risk. For example, much of the equity premium puzzle occurs during the years after the Depression. The Depression generation has been reported to be very "stock averse", perceiving equity to be much riskier than later generations do.