Topic IIE: A New Approach to Loss Aversion
Koszegi & Rabin (2006)
:
They develop a new and improved theory of
referencedependent utility with loss aversion.
Speci
fi
cally, they address two major issues — two
“loopholes” in the existing approach:
(1) What determines the reference point?
(2) When do people experience loss aversion, and
what is the magnitude of this experience?
They address these issues by incorporating two novel
features:
(1) A person’s reference point is her recent beliefs or
expectations about outcomes.
(2) Gainloss utility is directly tied to the intrinsic utility
from consumption — so that a person experiences more
gainloss utility for goods that involve more consumption
utility.
1
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Model
:
Suppose there are
N
goods:
Person chooses a vector
(
x
1
, x
2
, ..., x
N
)
.
Reference point is a vector
(
r
1
, r
2
, ..., r
N
)
.
Preferences are:
Total Utility
≡
N
X
i
=1
[
w
i
(
x
i
) +
v
i
(
x
i

r
i
) ]
.
•
w
i
(
x
i
)
is intrinsic utility for good
i
.
•
v
i
(
x
i

r
i
)
is gainloss utility for good
i
.
How to formalize that gainloss utility is directly tied to
intrinsic utility:
Assume there exists a “universal gainloss function”
μ
(
z
)
such that for each good
i
, gainloss utility is
v
i
(
x
i

r
i
) =
μ
(
w
i
(
x
i
)
−
w
i
(
r
i
) )
.
In general,
μ
(
z
)
takes form of the KahnemanTversky
value function.
We’ll focus on the special case:
μ
(
z
) =
(
η
z
if
z
≥
0
ηλ
z
if
z
≤
0
2