of dividend growth to drive the P/D ratio: restating the argument of Shiller
(1981) and LeRoy and Porter (1981), if these forecasts are indeed rational,
it must be that P/D ratios predict cash-flow growth in the time series, which
they do not.^19 Nor can we use changing forecasts of future risk-free rates:
again, if the forecasts are rational, P/D ratios must predict interest rates in
the time series, which they do not. Even changing forecasts of risk cannot
work, as there is little evidence that P/D ratios predict changes in risk in the
time series. The only story that remains is therefore one about changing
risk aversion, and this is the idea behind the Campbell and Cochrane
(1999) model of aggregate stock market behavior. They propose a habit for-
mation framework in which changes in consumption relative to habit lead
to changes in risk aversion and hence variation in P/D ratios. This variation
helps to plug the gap between the volatility of dividend growth and the
volatility of returns.
Some rational approaches try to introduce variation in the P/D ratio
through the third term on the right in Eq. (14). Since this requires investors
to expect explosive growth in P/D ratios forever, they are known as models
of rational bubbles. The idea is that prices are high today because they are
expected to be higher next period; and they are higher next period because
they are expected to be higher the period after that, and so on, forever.
While such a model might initially seem appealing, a number of papers,
most recently Santos and Woodford (1997), show that the conditions under
which rational bubbles can survive are extremely restrictive.^20
We now discuss some of the behavioral approaches to the volatility puz-
zle, grouping them by whether they focus on beliefs or on preferences.
4.2.1. beliefsOne possible story is that investors believe that the mean dividend growth
rate is more variable than it actually is. When they see a surge in dividends,
they are too quick to believe that the mean dividend growth rate has in-
creased. Their exuberance pushes prices up relative to dividends, adding to
the volatility of returns.
A story of this kind can be derived as a direct application of representa-
tiveness and in particular, of the version of representativeness known as the
32 BARBERIS AND THALER
(^19) There is an important caveat to the statement that changing cash-flow forecasts cannot
be the basis of a satisfactory solution to the volatility puzzle. A large literature on structural
uncertainty and learning, in which investors do not know the parameters of the cash-flow pro-
cess but learn them over time, has had some success in matching the empirical volatility of
returns (Brennan and Xia 2001, Veronesi 1999). In these models, variation in price/dividend
ratios comes precisely from changing forecasts of cash-flow growth. While these forecasts are
not subsequently confirmed in the data, investors are not considered irrational—they simply
don’t have enough data to infer the correct model. In related work, Barsky and De Long
(1993) generate return volatility in an economy where investors forecast cash flows using a
model that is wrong, but not easily rejected with available data.
(^20) Brunnermeier (2001) provides a comprehensive review of this literature.