Hoisted from the Archives from Nine Years Ago: My Critique of Barro-Reitz on Rare Events and the Equity Premium
New Economist writes:
New Economist: Has Barro solved the equity premium puzzle? : 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.... 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
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.
I think Barro has missed something important. Finance economists talk of the equity premium as a suspiciously low price of stocks relative to the prices of risk-free real bonds. But that's not really correct. In the real world, the equity premium takes the form of a suspiciously low price of stocks relative to *short-term nominal government bonds.* To say that stock prices relative to nominal bond prices can be explained by the risk of disaster--having a Great Depression or becoming the battleground in a World War--requires that the real value of nominal government bonds not be affected by such a disaster. Yet one standard response of governments to the budget crisis brought on by disaster is inflation.
In order to make Barro's theory work, you need a (1) significant probability of (2) economic disaster that nevertheless (3) does not lead to significant inflation and (4) does not lead to a formal government default. Besides the Great Depression itself, it's hard for me to think of a disaster in the past that fits those four requirements. Typically, inflation means that economic disasters that reduce stock values also reduce real bond values as well: the 1% disaster that removes half your capital stock and cuts real GDP in half also needs to leave the price level and the government's commitment to repaying its bonds unaffected.
