A (Graduate) Teaching Note on Barro's (2005) "Rare Events and the Equity Premium" and Rietz's (1988) "The Equity Premium: A Solution"
Robert Barro should have called his 2005 "Rare Events and the Equity Premium" paper something like "Rare Events and the Low Riskfree Rate" instead...
Barro's paper follows Rietz (1988) and uses the possibility of future disastrous falls in economy-wide consumption and in payouts on equities to explain the high premium equity return relative to bonds, and the low real return on bonds as well.
The primary channel is not what you probably think: it is not that the fear of future catastrophe depresses the price and hence raise the in-sample--we here in the United States haven't seen the real catastrophes the lurk out there--average return to equities.
The primary channel is that fear of future catastrophe raises desired savings to carry purchasing power forward in time in case of need. But, since assets are in fixed supply in the Lucas-tree model Barro uses, this outward shift in savings demand drives the prices of real bonds up and the returns on real bonds down. It also--for risk-aversion parameters greater than one--drives the prices up and the returns down on equities as well (but not as much). A greater fear of future catastrophe is a source of high, not low, price-dividend and price-earnings ratios.
Hence the story implicit in Barro (2005): the implicit story is that stock market multiples were much higher in 1999 and 1929 than they were in 1982 and 1922 because the likelihood of a macroeconomic catastrophe greater than the Great Depression was much higher in 1999 and 1929 than it was in 1982 and 1922. Hence people were desperate to save for the future to insure against the greater likelihood of macroeconomic catastrophe. And that was the force underpinning the 1990s stock market boom.
This is, I think, a trap set for us by using the Lucas-tree model as a workhorse. Its lack of production and accumulation is, I think, a much bigger drawback than is sometimes recognized...
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