Has Barro solved the equity premium puzzle?

It's not quite the holy grail of financial economics, but certainly one of the longest running debates has been over what is known as the equity premium puzzle - or why US stock returns are so much higher than returns on Treasury bonds. The seminal paper was by Rajnish Mehra and Edward C.Prescott in 1985: "The Equity Premium: A Puzzle" (PDF), published in the Journal of Monetary Economics. Mehra and Prescott showed it was difficult to reconcile empirical facts about equity and debt returns with reasonable assumptions about the relative rate of risk aversion and the pure rate of time preference, posing difficulties for the capital asset pricing model.

A new paper by Robert Barro to this year's Minnesota Workshop in Macroeconomic Theory attempts to answer the puzzle: Rare Events and the Equity Premium (PDF). Barro's paper builds upon a 1988 JME article by Thomas Rietz entitled "The equity premium: A solution" (sorry, no PDF available), which argued that the premium could be explained by infrequent but very large falls in consumption (i.e. wars, depressions or disasters), if the intertemporal elasticity of substitution of consumption is low. Or as Brad DeLong recently put it:

Rietz's (1988) answer to the equity premium puzzle was this: a long, fat lower tail to the return distribution. A small probability of very bad things happening to stock returns could support both (a) a relatively small sample variance of returns, and (b) rational aversion to large-scale stock ownership large enough to produce the observed equity premium. The question that Rietz was unable to answer was: "What exactly are these very bad things?"

Mehra & Prescott immediately dismissed the Rietz arguments in a 1988 JME article (PDF), concluding:

Are Rietz's disaster scenarios reasonable? They are undoubtedly extreme. That such extreme assumptions are needed to account for the average returns on debt and equity we interpret as supporting our contention that standard theory still faces an unsolved puzzle.

But Barro has resurrected Rietz, and added his own twist. Barro explained the origins of his 2005 paper in an interview just published by the Minneapolis' Fed's journal, The Region:

Mehra and Prescott were extremely critical of the Rietz analysis, and I think they managed to convince most people that low-probability disasters were not the key to the equity premium puzzle. But, although I highly value the insights in their original 1985 paper (which Mehra and Prescott like to point out was actually written in 1979), I think the arguments in their 1988 comment on Rietz were incorrect.

I had not thought much about this issue until a few months back—it's not an area that I've worked in. But when I began to study it, it seemed that low-probability disasters could be quite important. And then I found Rietz's paper, which I thought was a great insight, and I have been building on it. Frankly, I think this idea explains a lot. Of course, there is a good deal more to work out, to think about further, but I think his basic insight is correct.

He elaborates:

Suppose that you have potential events with, say, a 1 percent annual probability, where you lose half of your capital stock and GDP. This possibility seems to be enough to get something like the observed equity premium. Moreover, this mechanism has implications for a lot of other variables, not just for the excess of the average return on stocks over the return on government bills. For example, it can explain the very low “risk-free” rate and low expected real interest rates during most U.S. wars back to the Civil War. It can also explain some of the evolution of price-earnings ratios for the U.S. stock market.

...I've looked at the 20th century history of large, short-term economic contractions as a way of motivating the general orders of magnitude for the parameters in the model. So, looking at the world wars and the Great Depression, and other depressions—for example, in Latin America and Asia in the post-World War II period—you find a substantial number of these events. If you take that whole history covering many countries over 100 years, you get some idea of the probability and potential size of these rare disasters. I show in the model that if you use these “reasonable” parameters, the theoretical results match up with empirical observations, such as the equity premium.

Brad DeLong disagrees with this line of reasoning, arguing that in order for Rietz to be correct:

Any macroeconomic factor to drive the equity premium must therefore be a factor that leaves the real value and real return on short-period U.S. Treasury securities unaffected. But almost all true macroeconomic disasters that could halve or do worse to the real value of equities are likely to produce at the very least rapid and substantial inflation, if not confiscatory taxes on or outright repudiation of government bonds.

An economic depression would be deflationary, surely? As for war, while one can see how tight capacity constraints would be inflationary, Barro argues in The Region interview that real bond yields were actually low during wartime:

...I argue that this approach can explain a lot of the real-interest-rate movements in the U.S. history—particularly why expected real interest rates were very low during the main wartime periods in the United States, including the Civil War, World War I, World War II and the Korean War.

This is a fascinating debate that will likely not conclude anytime soon. For example, Cyber Libris blog recently raised two issues about the Rietz/Barro argument that merit consideration:

Two intertwined things worry me though. First, the Rietz/Barro argument sounds like the quantum leap debate in physics (disclosure: My field is not physics!). A lot of the literature in the economics of risk and uncertainty has provided evidence that people usually underestimate low probability events (from Howard Kunreuther to Nassim Taleb's famous Black Swan, click here for a video of Taleb). People have a hard time moving from the "normal" to the "rare" and back. How come that things (chief among them behaviors) are not the same in the small and in the large? So, who's right? Those who believe in the Black Swan or those who don't? More work is needed and it does not relate to finance only (think of climate events etc...).

Second, University of California Philippe Jorion and Yale University William N Goetzmann have shown that when you gather more data from more markets (outside the US) you get an empirical premium that is lower than the one that has been estimated on the US market only. Question: How do you reconcile the two sets of observations and arguments? In other words, is the premium too low or too high, is it vanishing and what kind of premium level should we expect in the future?

For related research, see Martin Weitzman's paper to an NBER seminar in April, A Unified Bayesian Theory of Equity 'Puzzles' (PDF), cited by Brad. While I have not yet given this paper the close reading it deserves, Barro and Weitzmann appear to be making quite similar arguments. Weitzman's paper concludes:

In expositions of the equity premium, risk-free rate, and excess volatility puzzles, the subjective distribution of future growth rates has its mean and variance calibrated to past sample averages. This paper shows that proper Bayesian estimation of uncertain structural growth parameters adds an irreducible fat-tailed background layer of uncertainty that can explain all three puzzles parsimoniously by one unified theory.

For those new to the topic and needing background, bibliographies of the equity premium debate can be found here (PDF) and here (hat tip: Cyber Libris).

Also worth reading, for a different slant on the issue, is the recent Economists' Voice paper by Simon Grant and John Quiggin, What Does the Equity Premium Mean? (free with trial registration). The authors argue that taking the equity premium seriously implies that "recessions are extremely costly even if they don’t lower average consumption." John Quiggin writes on his weblog that:

We also show that, to the extent that the equity premium is due to various kinds of capital market failure, it provides a rationale for public ownership of some business enterprises and for a rate of return on public investment close to the real bond rate.

UPDATE: See my follow up post, More thoughts on the equity premium puzzle, for a summary of views by Tyler Cowen, Brad DeLong, the Washington Monthly's Kevin Drum, Stephen Gordon and Winterspeak on this post.

UPDATE 2: In december 2005 Robert J. Barro posted a revised and retitled version of his equity premium paper, Rare disasters and asset markets in the twentieth century (PDF). Its scope is even more ambitious, seeking to explain not just the equity premium puzzle, but also the low risk-free rate, volatile stock returns, and why US interest rates have been low during major wars. Here is the new abstract:

The potential for rare economic disasters explains a lot of asset-pricing puzzles. I calibrate disaster probabilities from the twentieth century global history, especially the sharp contractions associated with World War I, the Great Depression, and World War II. The puzzles that can be explained include the high equity premium, low risk-free rate, and volatile stock returns. Another mystery that may be resolved is why expected real interest rates were low in the United States during major wars, such as World War II.

The model, an extension of Rietz [1988], maintains the tractable framework of a representative agent, time-additive and iso-elastic preferences, and complete markets. The results hold with i.i.d. shocks to productivity growth in a Lucas-tree type economy and also with the inclusion of capital formation.

Comments

[Don Lloyd]

I find it strange that the economic, political and demographic environment for a given dataset can simply be ignored. Is it not worth at least a mention that stocks and government bonds have recorded long term returns that move in opposite directions in the face of increasing demand for investments of all kinds?

http://catallarchy.net/blog/archives/2005/09/19/equity-premium-puzzle/

Regards, Don

[Peter Vermeulen]

Morgan Stanley has presented a valuation for equities based on Barro's paper. It is in the September 12 weekly (of David Miles, Vladimir Pilonka and Melanie Baker): What Hould Equities Be Worth in a Risky World.

I think the theory of barro is in agreement with the behavioral finance theory of James Montier (of Dresdner K.B.>). He states that humans have two kinds of reactions: slow ones based on the rational part of our brains and fast ones based on the emotional part of our brains.
This fast part have all animals. It is necessary for animals to take care for extremely dangerous rare events to survive. It is better to fly 100 times for danger that after scrutiny wasn't so dangerous than to forget one time to fly when the animal is eaten or something else that is fatal.
For your invested money to survive for a very long time (for example 50 years) it is also necessary to take care for extreme events. If you lose everything it is often no longer possible to get rich again. Over a time period of one year it is very unlikely that a rare event will happen, but over a time span of 50 years this kind of events that Barro present have a probability of maybe 30% or maybe higher.
So it is quite natural that also humans give exteme weight to very dangerous events. And of course, you can make money when you have the time to find out at a rational way that the danger doesn't exist or is exaggerated (for example after a terrorist attack)

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[Ben Sykes]

See the paper by Yogo in the April 2006 volume of the Journal of Finance. Yogo appears to nail the premium down.

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