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Farm Portfolio Problem: Part II
Lecture XIII
I.
Hazell, P.B.R. “A Linear Alternative to Quadratic and Semivariance Programming
for Farm Planning Under Uncertainty.”
American Journal of Agricultural Economics
53(1971):5362.
A.
This article is the basis for the application of MOTAD (Minimize Total
Absolute Deviation) in agriculture.
1.
Hazell’s approach is two fold.
He first sets out to develop review
expected value/variance as a good methodology under certain
assumptions.
2.
Then he raises two difficulties.
a.
The first difficulty is the availability of code to solve the
quadratic programming problem implied by EV.
b.
The second problem is the estimation problem.
Specifically,
the data required for EV are the mean and the variance matrix.
However, the variance matrix is an artifact of the assumption
of normality.
B.
The crux of the estimation problem is that the covariance terms in the EV
formulation are estimated by:
xx
s
cg
c
g
jk
h
j
j
h
k
k
h
s
k
n
j
n
1
1
1
1
1
−
−−
=
=
=
∑
∑
∑
()
(
)
where
j
x
is the level of activity
j
in the portfolio,
hj
c
is the observed return
on asset
j
at time
h
,
j
g
is the expected return on asset
j
,
s
is the number
of observations, and
n
is the number of assets.
This equality can be
reformulated as:
σ
2
11
2
1
1
1
=
−
−
==
=
∑∑
∑
s
cx
gx
hj
j
j
n
jj
j
n
h
s
.
Hazell suggests replacing this objective function with the mean absolute
deviation
A
s
x
hj
j
j
j
n
h
s
=−
=
=
∑
∑
1
1
1
.
Thus, instead of minimizing the variance of the farm plan subject to an
income constraint, you can minimize the absolute deviation subject to an
income constraint.
Another formulation for this objective function is to let
each observation h be represented by a single row
yc
g
x
yy
x
hh
j
j
j
j
n
h
j
j
n
−=
−
=
+−
=
∑
∑
1
1
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View Full Document AEB 6182– Agricultural Risk Analysis and Decision Making
Fall 2004
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This note was uploaded on 07/15/2011 for the course AEB 6182 taught by Professor Weldon during the Fall '08 term at University of Florida.
 Fall '08
 Weldon

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