Agriculture Reference
In-Depth Information
tend to not have fixed fee components, although there is often sharing of input costs. Also,
as mentioned earlier, one extreme contract form—fixed wage farmers—is generally not
present in modern North American farming. As a result, the relevant choice of farmland
contract is between a fixed cash rent contract
(s
=
β>
1and
0) and pure cropsharing contract
0).
Although it is not crucial to the empirical tests we perform, it is useful to make a
slight modification to the standard risk-sharing model to generate predictions about discrete
contract choices.
13
To do this, the model of contract choice between cash rent and cropshare
requires differential costs of the two contract regimes. We assume that each contract entails
a fixed “contract cost” (
(
0
<s<
1 and,
β
=
C
s
>C
c
.
Share contracts are likely to have higher costs because they require division and monitoring
of both the shared output that is susceptible to theft and the inputs that are provided under
moral hazard incentives.
14
In a cash rent contract
C
c
and
C
s
), which is largest for share contracts; that is,
s
c
=
1 and the farmer chooses the first-best
e
∗
=
(
effort level,
1
−
c
1
)/c
2
, so the total expected contract value is
V
c
=
e
∗
−
c
0
+
c
1
e
∗
+
(c
2
/
)(e
∗
)
2
]
2
−
C
c
.
[
2
−
(R/
2
)σ
(6.4)
<s
s
<
e
=
e(s)
=
(s
−
c
1
)/c
2
<e
∗
, so the expected contract
In a share contract, 0
1 and
value is
V
s
=
e(s
s
)
−
2
]
)(s
s
)
2
2
−
C
s
.
[
c
0
+
c
1
e(s)
+
(c
2
/
2
)(e(s))
−
(R/
2
σ
(6.5)
2
, the
For our purposes, the parameters of interest are the variance of the random input,
σ
farmer's risk preferences,
R
, and the farmer's wealth,
W
. Two predictions follow:
2
) increases, it is more likely that a share contract
σ
PREDICTION 6.5
As output variability (
will be chosen over a cash rent contract.
PREDICTION 6.6 Under declining absolute risk aversion, as farmer wealth increases, it is
more likely that a cash rent contract will be chosen over a cropshare contract.
Prediction 6.5 is the classic risk-sharing prediction, and the one to which we devote much
of our attention. It is proven by examining the comparative statics of these indirect objective
functions. The ratio
V
c
/V
s
is decreasing in
2
. This follows from
∂V
c
/∂σ
2
σ
=−
(R/
2
)
∂V
s
/∂σ
2
2
, so both
V
c
and
V
s
are decreasing in
2
.For
s
∗
∈
(
and
=−
(R/
2
)s
σ
0, 1
)
it
V
c
declines more rapidly than
V
s
. Prediction 6.6 can be proven in a similar
follows that
V
c
/V
s
is decreasing in
∂V
c
/∂R
=−
(σ
2
manner. The ratio
R
. This follows from
/
2
)
and
∂V
s
/∂R
=−
(s
2
2
V
c
and
V
s
are decreasing in
s
∗
∈
(
σ
)/
2, so both
R
.For
0, 1
)
, it follows
V
R
declines more rapidly than
V
s
. The ratio
V
c
/V
s
is increasing in
that
W
. This follows
just shown.
15
The general incentive
structure of this risk-sharing model is laid out in table 6.2.
R
(W)<O
from
and the direct effect of changes in
R
