These numbers are very similar to those used by Mehra and Prescott (1985)
and Constantinides (1990).
The investor’s preference parameters are γ, ρ, λ, k, and b 0. We choose the
curvature γof utility over consumption and the time discount factor ρso as
to produce a sensibly low value for the risk-free rate. Given the values of gC
and σC, Eq. (23) shows that γ=1.0 and ρ=0.98 bring the risk-free interest
rate close to Rf− 1 =3.86 percent.
The value of λdetermines how keenly losses are felt relative to gains in
the case where the investor has no prior gains or losses. This is the case that
is most frequently studied in the experimental literature: Tversky and Kah-
neman (1992) estimate λ=2.25 by offering subjects isolated gambles, and
we use this value.
The parameter kdetermines how much more painful losses are when they
come on the heels of other losses. It is an important determinant of the in-
vestor’s averagedegree of loss aversion over time. In the results that we pres-
ent, we pick kin two different ways. Our first approach is to choose kso as
to make the investor’s average loss aversion close to 2.25, where average
loss aversion is computed in a way that we make precise in the Appendix.
After prior gains, the investor does not fear losses very much, so his effective
loss aversion is less than 2.25; after prior losses, he is all the more sensitive
to additional losses, so his effective loss aversion is higher than 2.25, to a de-
gree governed by k. We find that choosing k=3 keeps average loss aversion
close to 2.25. To understand what a kof 3 means, suppose that the state
variable ztis initially equal to 1, and that the stock market then experiences
a sharp fall of 10 percent. From equation (10) with η=1, this means that zt
increases by approximately 0.1, to 1.1. From (8), any additional losses will
now penalized at 2.25+3(0.1)=2.55, a slightly more severe penalty.
Our second approach to picking kis to go to the data for guidance: we
simply look for values of kthat bring the predicted equity premium close to
its empirical value.
The parameter b 0 determines the relative importance of the prospect util-
ity term in the investor’s preferences. We do not have strong priors about
248 BARBERIS, HUANG, SANTOS
Table 7.1
Parameter Values for Economy IParameter
gC 1.84%
σC 3.79%
γ 1.0
ρ 0.98
λ 2.25
k (range)
b 0 (range)
η 0.9