Barro, Robart J, “Rare Disasters and Asset Prices in the Twentieth Century,” The Quarterly Journal of Economics Vol. 121 No. 3 (2006), 823-866.
Mehra and Prescott (1985) find an equity premium puzzle, which is that either
- the observed equity premium and volatility imply very high consumer risk aversion, or
- a more reasonable level of risk aversion would imply a risk free rate that is higher and more variable than the one we see in the data.
At a very high level, Barro and others attempt to solve the puzzle by introducing more risk into their models. Rather than suggesting that consumers are indeed extremely risk averse, they allow risk aversion to be low but suggest Mehra and Prescott simply didn’t account for enough risk. This explanation is extremely intuitive and flexible enough, I think to encompass a wide variety of methods for adding risk. So, I find the first few pages of this article instructive. The probability of a rare disaster could certainly be something consumers have in mind. The logic is solid. The rest of the paper discusses a calibration that I find unconvincing at best.
The problems with the calibration are as follows.
- Barro relies on a very small sample of rare disasters. Although he cites 60 instances, they can mostly be reduced to four “events”: WWI, WWII, the Great Depression, and two decades of revolutions in South America. It is difficult to believe that anything can be inferred from the timing of these occurrences.
- In order to make inferences, Barro relies on three very strong assumptions, which are that (1) events of major social unrest are uncorrelated with one another, that (2) they are randomly and uniformly distributed across countries, and that (3) they are randomly and uniformly distributed across time. This third assumption means that the probability of disaster is constant across time.
- Finally, Barro conflates consumption and expenditures. In other words, there are no durable goods and the representative consumer has zero savings. When GDP falls, Barro assumes that consumption also falls and so expected stock returns must be high to offset this risk. Durable goods and savings are two methods that consumers can use to smooth actual consumption.
Barro’s base model is meant to be simple, and he does acknowledge in closing that stochastic default probability would be an obvious way to extend the model. I can allow for the theoretical limitations. The calibration, however, I find too incredible to be very useful. If anything, he shows that a 1.7% chance of a bad event is about the right amount of extra risk to solve the equity premium puzzle. He is not convincing that 1.7% is anywhere close to the actual probability of another world war or communist revolution.