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Friday, September 30, 2005

New Economist on Barro and the Equity Premium Puzzle

New Economist wonders if Barro has solved the equity premium puzzle:

New Economist: 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's in 1985: "The Equity Premium: A Puzzle" (PDF) 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 Thomas Rietz 1988 JME article "The equity premium: A solution", 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.

Barro explained his 2005 paper's origins in an interview in the September 2005 issue of 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 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 capacity constraints would be inflationary, Barro argues that real bond yields were 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:

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. 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 background, bibliographies of the equity premium debate can be found here (PDF) and here (hat tip: Cyber Libris).

Worth reading for a different perspective is the new Economists' Voice paper by Simon Grant and John Quiggin, What Does the Equity Premium Mean? 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:  Brad DeLong comments on Barro here.

    Posted by on Friday, September 30, 2005 at 01:16 AM in Academic Papers, Economics, Financial System | Permalink  TrackBack (0)  Comments (0)


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