Brad de Long points to a piece on the equity premium by Marty Weitzman and says,
Marty Weitzman is smarter than I am …This is brilliant. I should have seen this. I should have seen this sixteen years ago. I *almost* saw this sixteen years ago.
Weitzman’s idea[1] is the replace the sample distributions of returns on equity and debt with reasonable Bayesian subjective distributions. These have much fatter tails, allowing for a higher risk premium, lower risk free rate and higher volatility, in the context of a socially optimal market outcome. Here are some of the reasons why this is important
My immediate reaction is the same as Brad’s. Something like this has occurred to me too, but I’ve never thought hard enough or cleverly enough about it how to work it out properly. This is a very impressive achievement, and Marty Weitzman is very, very smart (which we already knew).
My second reaction is a little more sceptical. Some previous attempts at resolving the equity premium have focused on the tails of the distribution, and the possibility of catastrophic loss. Tthe problem was that it was difficult to describe an outcome where the return on equity was large and negative, but bonds were still a safe asset. The various catastrophic examples cited, such as hyperinflation, revolution and nuclear war all failed in this respect.
Applying the same reasoning to Weitzman’s argument, we need to consider whether there is a reasonable model of a stable capitalist economy, with functional financial markets, that produces a negative long-run rate of growth in outptu per person. The only one I can imagine is based on resource exhaustion, and I can’t really see belief (positive probability weight) in such a model being widespread enough to generate the observed equity premium. With less confidence, I’d assert that there are pretty good technological reasons to rule out a sustained rate of productivity growth (embodied and disembodied) of more than 5 per cent, for countries that are already at the frontier. The maximum sustainable rate of growth of output per person cannot be much above this.
I haven’t been able to check the math, but I doubt that a complete Bayesian explanation of the equity premium puzzle can be obtained if the prior distribution on the long-run rate of growth is bounded in this way.
My third reaction is eclectic. My general view is that there is no one explanation of the equity premium, but a set of problems with the standard consumption-based model of asset pricing (CCAPM) that interact to produce results radically different from those of the model. Making expectations Bayesian rather than classical will amplify the effects of any other deviation in the model, and therefore fit neatly into this story.
fn1. The only version of the paper I’ve seen so far is a PDF file in which the maths has not come through. But I think I’ve got the basic idea.
John Quiggin 
John, tracking back to your earlier comments on the implications of the equity premium puzzle, you seem to limit the idea of govt participation in the economy to ownership of enterprises. There’s also share investment, which the govt can hold at arms length in a portfolio. Like you, what got me started thinking in this way was not the theory but observing the RBA doing something that Tobin spoke of – participating in markets so as to make them more rational. I am thinking of the RBA’s contrarian behaviour on the foreign exchange markets during the 1980s in particular. This was very benign. It smoothed peaks and troughs in the foreign exchange markets (improving their efficiency) and it made a pot of money for the Government. It stopped making so much money I think at around the time it came up with a very different additional strategy of ‘smoothing and testing’ (which may be sensible but seems pretty bereft of any well thought through theoretical foundation to me).
I have always thought there was a case for governments doing this more broadly in other markets. I’ve argued elsewhere that governments could do something similar by holding more debt and equity and also varying their exposure in a contrarian and countercyclical direction.
John
I still havn’t grasped why the Baysian assumption is so important vis a vis the Gaussian assumption. They both cater for fat tails.
Catering for fat tails or not – the distributions of expected return and of risk variance are not normal – they are partitioned. Which is why the Bayesian assumption is important.
Simon Grant and I looked at share ownership in the context of social security
Grant, S. and Quiggin, J. (2002), ‘The risk premium for equity: implications for Clinton’s proposed diversification of the social security fund’, American Economic Review 92(5), 1104-15.
Tipper, the point, if I have it right, is that a Bayesian subjective distribution derived from a given set of sample data will have fatter tails than the sample distribution itself.