00Thaler_FM i-xxvi.qxd

and where for zt≤1,

(15)

and for zt>1,

(16)

with

λ(zt)=λ+k(zt−1). (17)
Equations (15) and (16) are pictured in figure 7.1. Finally, the dynamics
of the state variable ztare given by

(18)

We calculate the price Ptof a dividend claim—in other words, the stock
price—in two different economies. The first economy, which we call “Econ-
omy I,” is the one analyzed by Lucas (1978). It equates consumption and
dividends so that stocks are modeled as a claim to the future consumption
stream.
Due to its simplicity, the first economy is the one typically studied in
the literature. However, we also calculate stock prices in a more realistic
economy—“Economy II”—where consumption and dividends are modeled
as separate processes. We can then allow the volatility of consumption
growth and of dividend growth to be very different, as they indeed are in
the data. We can think of the difference between consumption and divi-
dends as arising from the fact that investors have other sources of income
besides dividends. Equivalently, they have other forms of wealth, such as
human capital, beyond their financial assets.
In our model, changes in risk aversion are caused by changes in
the level of the stock market. In this respect, our approach differs from
consumption-based habit formation models, where changes in risk aver-
sion are due to changes in the level of consumption. While these are dif-
ferent ideas, it is not easy to illustrate their distinct implications in an
economy like Economy I, where consumption and the stock market are
driven by a single shock, and are hence perfectly conditionally correlated.
This is why we emphasize Economy II: since consumption and dividends
do not have to be equal in equilibrium, we can model them as separate pro-
cesses, driven by shocks that are only imperfectly correlated. The contrast

zz

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240 BARBERIS, HUANG, SANTOS