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Mehra and Prescott’s Equity
Premium Puzzle
•
Can the 6% equity premium over riskless debt be explained using a version
of the stochastic growth model?
•
Answer: No. A good illustration of a quantitative exercise.
1
Environment
Just a growth version of Lucas (1978)
•
Preferences
U
(
c
)=
c
1
−
ψ
1
−
ψ
•
Technologies (Endowments vary stochastically according to an
n
state
Markov process in
growth rates
):
y
t
+1
=
x
t
+1
y
t
where
x
t
+1
∈
{
λ
1
, ..., λ
n
}
and
π
ij
=Pr[
x
t
+1
=
x
j

x
t
=
x
i
]
2
Equilibrium Asset Pricing
Just as in Lucas:
p
t
=
βE
"
μ
y
t
y
t
+1
¶
ψ
(
y
t
+1
+
p
t
+1
)

x
t
,y
t
#
(1)
⇐⇒
P
(
y,i
)=
β
n
X
j
=1
π
ij
μ
y
λ
j
y
¶
ψ
[
λ
j
y
+
P
(
λ
j
y,j
)]
•
Clearly
P
(
y,x
) is homogeneous of degree one in
y
:T
oseeth
i
s
,
P
(
γy,i
)=
β
n
X
j
=1
π
ij
μ
1
λ
j
¶
ψ
[
λ
j
γy
+
P
(
λ
j
γy,j
)] =
γP
(
y,i
)
•
Given that
P
(
y,x
) is homogeneous of degree 1, then conjecture a solution
of the form
P
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 Spring '07
 CORBAE

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